27 May Maths 1

MATHS Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

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You want to construct boundary to your land. Your land has semi circular shapes attached to a square on all four sides. One side of the square is 7 meters. What will be your cost of boundary making @ Rs. 1 per meter?

• There are four semicircular shapes. Each having diameter of 7 meters. Thus we have to calculate circumference of two squares. Thus we have to calculate 4 pi *7/2 = 44 . So my cost will be Rs. 44 Ans. www.afterschoool.tk

A copper Ball (sphere) of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of wire?

• You need formulae of cylinder (wire) and formulae of sphere(ball) to calculate it. 4/3 pi 9*9*9 = pi*.2*.2*h • Solving this we get: 4*9*9*3/ .2*.2 • H = 24300 cm. or 243 meters . Ans. •

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Find the number of lead balls of diameter 1 cm each that can be made from a sphere of diameter 16 cm? • The volume of big sphere is: 4/3pi*8*8*8, volume of small lead ball is : 4/3*pi*.5*.5*.5. Now divide volume of big sphere by volume of small lead ball. It will give us number of bolls that we can make. Now we get: 16*16*16 = 4096 ans. www.afterschoool.tk

Two cubes are joined with each other. Find the total surface area of new cuboid. One side of earlier cube was 8 cm. What is its ratio to surface area of 2 cubes?. • The formulae of surface of cuboid is : 2(lb+lh+bh) so length is : 16, breadth = 8, height = 8. surface area is : • 2 (16*8 + 16*8 + 8*8) = 2(128+128+64) = 2(320) = 640 sq.cm. • Surface area of cube: 6*side *side: 6*64= 384 Sq. cm. for one, for two : 768. thus the ratio is: 640:768 or : 3:5 ans. www.afterschoool.tk

How many vertices are there is a cube? • 8

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How many faces are there is a cuboid? • 6

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How many edges are there is a cube? • 12

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I got a pipe painted (from outside only). It cost me 1760 Rs. @1 sq.meter. At a time, how much water can be there in this pipe- find the total volume of this pipe radius and height are in ratio of 7:10?

• Painting is done on curved surface area. Formulae of curved suface area is pi*r*l. pie*7x*square root of (70x^2) = 1760. = pie 58.3x =1760; • 184 x^2 =1760 approx. ; x = 2.2approx. • Volume: pi* 14*14*21 = 22*14*14*3 = 12936 cubic meters approx. • L = square root of 7x*10x www.afterschoool.tk

Base of a parallelogram is 5, its height is 10, what is its area? • Area = base * height • =10*5 = 50 • Ans.

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I have a kite, height of which is 12cm, and width of which is 10cm, what is the surface area of this kite?

• A kite is of the shape of rhombus. The area of rhombus = ½ diagonal *diagonal • The diagonals are given – (height and width are diagonals) • =1/2 (12*10) = 60 Sq. cm.

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I have to paint our class room. Length of afterschoool class room is 30 feet, and width is 22, height is 10 ft. what is cost of painting @ Rs. 20 per sq. ft. without deducting space of windows?

• Area of four walls: • 2(l+b)*h= 2 (30+22)*10 = 1040 sq.ft, cost :1040*20 = 20800 Rs. Ans.

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We have a painting which is of the shape of a trapezium. Find its surface area, if its two parrallel sides are of 10 and 12 cm and distance between them is 6cm?

• Formulae of trapezium area is: • ½ (sum of parrellel sides) * distance between them. • =1/2 (10+12) *6 • =66 sq. cm. Ans. www.afterschoool.tk

There is an equilateral triange of side 9 cm. there is one circle in this and one circle over it touching its sides. What are the radii of these circles? • Radius of in –circle: side / 2*3^1/2 • Radius of circum –circle = side / 3^1/2 • Radius of incircle: 2.64 cm approx. • Radius of outer circle: 5.29 approx. www.afterschoool.tk

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