Question 1

State true or false in the following statements:

1 . A sphere has radius 3 a units. A right circular cylinder has height 4 times its radius, which is a units. The ratio of the volume of the cylinder to the sphere is 1 : 9.

2 . Consider a circle with diameter d units and a square with diagonal d units. If ay crawls round the circle once and an ant crawls round the square once, the y travels further. 3. The volume of a right circular cone with height 15 cm is the same as the volume of a right circular cylinder with height 5 cm, if they both have the same radius.

4 . Suppose a sphere has a diameter of 10 cm. Suppose the height of a closed right circular cylinder is double its radius, and that its radius is the same as the radius of the sphere. The ratio of the surface area of the sphere to that of the cylinder is 2 : 3.

5 . If the diagonals of a quadrilateral intersect at right angles the quadrilateral must be a square or a rhombus or a kite.

6 . If the diameter and height of a right circular cone are equal then the lateral surface area of the cone is sqrt(5) pi. r^2 . where the radius is r and Lateral surface area of cone is the area of the sides only.

7 . If the photograph is enlarged by a scale factor of 3 it will t onto a piece of paper that measures 30 cm by 20 cm.

8 . If it is enlarged by a scale factor of 2,5 it will t onto a 30 cm by 20 cm piece of paper with no space left on the sides and 2,5 cm left at the top and at the bottom.

9 . If it is reduced by a scale factor of 0; 75 then four such photographs will cover the page with dimensions 30 cm by 20 cm, exactly.

Question 2

A square piece of material with sides 150 cm is used to make a circular table cloth. The diameter of

the completed cloth must be 1.2 m and 5 cm is provided for a hem. How much material is wasted?

Question 3

How deep must a circular swimming pool be if its volume is 64 000 litres and its diameter is 8 m? If the depth is x m, then ?