Second Term Maths

The smallest of three consecutive positive numbers is m. Three times the square of the largest is greater than the sum of the squares of the other two number by 67 .Find m The length of a rectangle exceeds its breadth by 4 centimeters. If the length were halved and the breath increase by 5cm the area would be decreased by 35 square centimeter . Find length of the rectangle A piece of wire which is 18 metres long and cut into two parts .The first part is bent to form the four sides of square. The second part is bent to form the four sides of a rectangle .The breadth of the rectangle is 1 metre and its length is x metres. If the sum of the areas square and rectangle is A square metre show A=16- 3x +x2/4 .IF A=9 calculate the value of x The diagram shows a section through a chemical flask consisting of a spherical body of

internal radius r cm with cylindrical neck of internal radius 1/6 r cm and length r cm .show that when fill to the brim the flask with hold approximately 77r3 /18 cm3 (The volumes enclosed by the sphere and cylinder overlap – between the dotted lines –but this fact may be ignored) A solid iron cone is 12 cm in height and radius of the circular base is 4cm .its placed on its base in a cylinderical vessel of iternal radius 5cm .water is poured into the cylinder untill the depth of water is 16 cm .the cone is removed .Find by how much the water level falls