9 June Maths Iii
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Maths Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
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The length of minute hand on a wall clock is 7cms. What is the area swept by the minute hand in 30 minutes?
• This is the question of circle • Area of circle : pi *r*r = 22/7*7*7=154 • But the area in 30 minutes will be half circle – so it will be 77 sq cm.
www.afterschoool.tk
A wheel makes 1000 revolution in covering a distance of 88 km. What is diameter of the wheel?
• The circumference of wheel = 88000 / 1000 = 88. • Formulae of circumference of circle = 2pi*r = 2*22/7*R = 88 • 2R = 88*7/22 = 28meters Ans.
www.afterschoool.tk
A wire is in the form of an equilateral triangle with area 5 sq. m. If its shape is changed to a circle, its radius will be? • Area of Triangle: 3^1/2/4 *side*side • 3^1/2/4 *side*side =5, • side^2 = 20/ 3^1/2 =11.5 Side = 3.4 approx. Length of wire:3*3.4= 10.2 Circumference of circle =10.2 2pi *r = 10.2 R = 10.2/ 6.28 = 1.63 meters approx.
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What is the circumference of semicircular shape on a line of length 10 cm? • • • •
Circumference = 2pi*r =2*22/7*5 =10*3.1428 = 31.42 Half of circumference = 15.92 Add diameter with this = 25.92 ans.
www.afterschoool.tk
The ratio of the length of a side of an equilateral triangle and its height is? • Let us assume that side of a triangle is X. its area is .433 X^2. (3^1/2/4 *side * side). Let us assume that we divide it in two triangles of equal size with area = .433 X^2/2. This triangle will have area ½*base*height. (being right angle triangle) • Here base = side /2, so • .433x^2 /2 =1/2*X/2*h • Height = .433x^2*4 /2x = .433 *2 X • Ratio of side to height = 1: .866 Ans. • Another method = applying pythogorus rule, • X^2 = (x/2)^2 + height ^2 , solving we get ratio of side to height as 2:3^1/2 www.afterschoool.tk
There are 4 circles in a bigger circle. The diameter of biggest circle is 56 but those of smaller circles is 7. what is area •of bigger circle which has not been occupied by smaller circles.
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Answer: • Area of bigger circle: • 3.1428*28*28 =2464 • Area of smaller circle = 22/7*7/2*7/2 = 38.5 ; there are four circles so area is 38.5*4 = 154 • Area of uncovered bigger circle • 2464-154 = 2310 ans. www.afterschoool.tk
Inner circumference of a 14 meter wide race track is 440 meters, what is the radius of outer circle?
• Inner radius is • 2pi*r = 440; r = 440*7/44 = 70 • Radius of outer circle is 70+14 = 84 ans.
www.afterschoool.tk
A circular wire of radius 42 cm is bent into the shape of a rectangle. What is the diagonal of this rectangle, if the sides are in the ratio of 6:5?
Step 1: find the circumference : 2*pi*r = 2*22/7*42 =264 6x+5x = 264; 11x=264; x =24 Length of rectangle : 144, width is 120. • Diagonal will be square root of 144^2 +120^2= 187.44 approx. • • • •
www.afterschoool.tk
What is the area of circle inscribed in an equilateral triangle of side 24? • • • • •
We know that radius of incircle is : R = Side /( 2*3^1/2) Therefore radius is : 24 / (2*1.73) =6.928 Area of circle = pie *r *r = 150.8 approx. ans.
www.afterschoool.tk
What is the area of circle circumscribed in an equilateral triangle of side 24?
• We know that radius of circumcircle is : • R = Side /3^1/2 • Therefore radius is : 24 / 1.73 • =14aprox • Area of circle = pie *r *r • = 196 pi. Ans. www.afterschoool.tk
A man builds a circular pool of radius 5 inside a circular garden of radius 12. In order to compensate for area lost, he extends the garden, What is radius of garden, if its area is same as earlier? • • • • • • • •
Area of garden: 144 pi. Area of pool=25 pi Let us assume that he increases radius by x Pi * (12+x)^2 -144pi = 25 pi. 144+24x+x^2-144 = 25 X^2+24x-25 =0 X^2 +25x-x-25; x(x+25)-1(x+25) X=1 New radius of the garden is 13 Ans.
www.afterschoool.tk
What is the area of largest triangle that can be inscribed in a semi-circle of radius 7?
• Here we will keep the base as diameter of the circle = 14. Height will be 7 (as radius). • Thus the area will be ½*7*14 • =49 ans.
www.afterschoool.tk
What is the area of largest triangle that can be inscribed in a circle of radius 7? • • • • •
Radius = side / 3^1/2 Side= Radius * 1.73 = 7*1.73 =12.12 Area of triangle: 3^1/2 /4 * 12.12*12.12 =63 approx. ans.
www.afterschoool.tk
What is the area of largest square that can be inscribed in a circle of radius 7? • Diagonal of square is 14. • Area of square is ½ *Diagonal * diagonal. • ½*14*14 = 98 ans.
www.afterschoool.tk
What is the area of largest hexagon that can be inscribed in a circle of radius 7? • Hexagon will have one side equal to radius = 7. • Hexagon is 6 multiplied to 3^1/2/4*side *side. • =21.21*6 • Area of hexagon = 127 approx.
www.afterschoool.tk
We don’t want a cow to graze more than 9856 sq m area in circular form. What should be the length of rope by which we should tether the cow?
• We have to calculate the radius in this question. • Pi*r *r = 9856 • R^2 =9856 / pi = 3136 • R = 56 ans.
www.afterschoool.tk
The ratio of radii of two circles is in the ratio of 1:2, what is the ratio of their area?
• 1:4 ans.
www.afterschoool.tk
The ratio of radii of two circles is in the ratio of 1:2, what is the ratio of their circumference? • 1:2 ans.
www.afterschoool.tk
The ratio of radii of two spheres in the ratio of 1:2, what is the ratio of their volume? • 1:8 ans.
www.afterschoool.tk
The ratio of sides of two cubes is in the ratio of 1:2, what is the ratio of their volume? • 1:8
www.afterschoool.tk
www.afterschoool.tk
www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs Most flexible, adaptive but rigorous programme Available in distance learning mode Case study focused- latest cases Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn • The only absolutely free course on internet • • • • •
www.afterschoool.tk
Workshops from AFTERSCHOOOL • • • • • • • • •
IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk
Flexible Specialisations: • • • • • • • • •
Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance
www.afterschoool.tk
Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who want to achieve success in life – not just a degree • Indepth knowledge and expertise • Professional approac: World class approach • Strong intellectual and business capabilities • Flexible – you may stay for a month and continue the rest of the education by distance mode. • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time • Placement for those who are interested
www.afterschoool.tk
Components Meditation, spiritualisation, and self development Business plan Essential softwares for business Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs • Editing of journals / newsletters • Consultancy / research projects • Assignments, communication skill workshops • • • • • • • •
www.afterschoool.tk
Pedagogy
• Case analysis • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits • Presentations • Group discussions and group projects • Periodic self assessment • Mentoring and counselling
www.afterschoool.tk
Branches • AFTERSCHOOOL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs. www.afterschoool.tk
Case Studies • We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs. www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
www.afterschoool.tk
The length of minute hand on a wall clock is 7cms. What is the area swept by the minute hand in 30 minutes?
• This is the question of circle • Area of circle : pi *r*r = 22/7*7*7=154 • But the area in 30 minutes will be half circle – so it will be 77 sq cm.
www.afterschoool.tk
A wheel makes 1000 revolution in covering a distance of 88 km. What is diameter of the wheel?
• The circumference of wheel = 88000 / 1000 = 88. • Formulae of circumference of circle = 2pi*r = 2*22/7*R = 88 • 2R = 88*7/22 = 28meters Ans.
www.afterschoool.tk
A wire is in the form of an equilateral triangle with area 5 sq. m. If its shape is changed to a circle, its radius will be? • Area of Triangle: 3^1/2/4 *side*side • 3^1/2/4 *side*side =5, • side^2 = 20/ 3^1/2 =11.5 Side = 3.4 approx. Length of wire:3*3.4= 10.2 Circumference of circle =10.2 2pi *r = 10.2 R = 10.2/ 6.28 = 1.63 meters approx.
www.afterschoool.tk
What is the circumference of semicircular shape on a line of length 10 cm? • • • •
Circumference = 2pi*r =2*22/7*5 =10*3.1428 = 31.42 Half of circumference = 15.92 Add diameter with this = 25.92 ans.
www.afterschoool.tk
The ratio of the length of a side of an equilateral triangle and its height is? • Let us assume that side of a triangle is X. its area is .433 X^2. (3^1/2/4 *side * side). Let us assume that we divide it in two triangles of equal size with area = .433 X^2/2. This triangle will have area ½*base*height. (being right angle triangle) • Here base = side /2, so • .433x^2 /2 =1/2*X/2*h • Height = .433x^2*4 /2x = .433 *2 X • Ratio of side to height = 1: .866 Ans. • Another method = applying pythogorus rule, • X^2 = (x/2)^2 + height ^2 , solving we get ratio of side to height as 2:3^1/2 www.afterschoool.tk
There are 4 circles in a bigger circle. The diameter of biggest circle is 56 but those of smaller circles is 7. what is area •of bigger circle which has not been occupied by smaller circles.
www.afterschoool.tk
Answer: • Area of bigger circle: • 3.1428*28*28 =2464 • Area of smaller circle = 22/7*7/2*7/2 = 38.5 ; there are four circles so area is 38.5*4 = 154 • Area of uncovered bigger circle • 2464-154 = 2310 ans. www.afterschoool.tk
Inner circumference of a 14 meter wide race track is 440 meters, what is the radius of outer circle?
• Inner radius is • 2pi*r = 440; r = 440*7/44 = 70 • Radius of outer circle is 70+14 = 84 ans.
www.afterschoool.tk
A circular wire of radius 42 cm is bent into the shape of a rectangle. What is the diagonal of this rectangle, if the sides are in the ratio of 6:5?
Step 1: find the circumference : 2*pi*r = 2*22/7*42 =264 6x+5x = 264; 11x=264; x =24 Length of rectangle : 144, width is 120. • Diagonal will be square root of 144^2 +120^2= 187.44 approx. • • • •
www.afterschoool.tk
What is the area of circle inscribed in an equilateral triangle of side 24? • • • • •
We know that radius of incircle is : R = Side /( 2*3^1/2) Therefore radius is : 24 / (2*1.73) =6.928 Area of circle = pie *r *r = 150.8 approx. ans.
www.afterschoool.tk
What is the area of circle circumscribed in an equilateral triangle of side 24?
• We know that radius of circumcircle is : • R = Side /3^1/2 • Therefore radius is : 24 / 1.73 • =14aprox • Area of circle = pie *r *r • = 196 pi. Ans. www.afterschoool.tk
A man builds a circular pool of radius 5 inside a circular garden of radius 12. In order to compensate for area lost, he extends the garden, What is radius of garden, if its area is same as earlier? • • • • • • • •
Area of garden: 144 pi. Area of pool=25 pi Let us assume that he increases radius by x Pi * (12+x)^2 -144pi = 25 pi. 144+24x+x^2-144 = 25 X^2+24x-25 =0 X^2 +25x-x-25; x(x+25)-1(x+25) X=1 New radius of the garden is 13 Ans.
www.afterschoool.tk
What is the area of largest triangle that can be inscribed in a semi-circle of radius 7?
• Here we will keep the base as diameter of the circle = 14. Height will be 7 (as radius). • Thus the area will be ½*7*14 • =49 ans.
www.afterschoool.tk
What is the area of largest triangle that can be inscribed in a circle of radius 7? • • • • •
Radius = side / 3^1/2 Side= Radius * 1.73 = 7*1.73 =12.12 Area of triangle: 3^1/2 /4 * 12.12*12.12 =63 approx. ans.
www.afterschoool.tk
What is the area of largest square that can be inscribed in a circle of radius 7? • Diagonal of square is 14. • Area of square is ½ *Diagonal * diagonal. • ½*14*14 = 98 ans.
www.afterschoool.tk
What is the area of largest hexagon that can be inscribed in a circle of radius 7? • Hexagon will have one side equal to radius = 7. • Hexagon is 6 multiplied to 3^1/2/4*side *side. • =21.21*6 • Area of hexagon = 127 approx.
www.afterschoool.tk
We don’t want a cow to graze more than 9856 sq m area in circular form. What should be the length of rope by which we should tether the cow?
• We have to calculate the radius in this question. • Pi*r *r = 9856 • R^2 =9856 / pi = 3136 • R = 56 ans.
www.afterschoool.tk
The ratio of radii of two circles is in the ratio of 1:2, what is the ratio of their area?
• 1:4 ans.
www.afterschoool.tk
The ratio of radii of two circles is in the ratio of 1:2, what is the ratio of their circumference? • 1:2 ans.
www.afterschoool.tk
The ratio of radii of two spheres in the ratio of 1:2, what is the ratio of their volume? • 1:8 ans.
www.afterschoool.tk
The ratio of sides of two cubes is in the ratio of 1:2, what is the ratio of their volume? • 1:8
www.afterschoool.tk
www.afterschoool.tk
www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs Most flexible, adaptive but rigorous programme Available in distance learning mode Case study focused- latest cases Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn • The only absolutely free course on internet • • • • •
www.afterschoool.tk
Workshops from AFTERSCHOOOL • • • • • • • • •
IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk
Flexible Specialisations: • • • • • • • • •
Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance
www.afterschoool.tk
Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who want to achieve success in life – not just a degree • Indepth knowledge and expertise • Professional approac: World class approach • Strong intellectual and business capabilities • Flexible – you may stay for a month and continue the rest of the education by distance mode. • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time • Placement for those who are interested
www.afterschoool.tk
Components Meditation, spiritualisation, and self development Business plan Essential softwares for business Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs • Editing of journals / newsletters • Consultancy / research projects • Assignments, communication skill workshops • • • • • • • •
www.afterschoool.tk
Pedagogy
• Case analysis • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits • Presentations • Group discussions and group projects • Periodic self assessment • Mentoring and counselling
www.afterschoool.tk
Branches • AFTERSCHOOOL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs. www.afterschoool.tk
Case Studies • We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs. www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
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