1. A solid cylinder has a total surface area of 231 cm2. It its curved surface area is two thirds of the total surface area, the volume of the cylinder is

2. What is its surface area of the sphere if the volume of the sphere is \(179\frac{2}{3}\) m3?

3. The area of a circular field is 3850m2. Find the cost of fencing the field at Rs.4 per meter.

4. A ladder reaches a window which is 24 m above the ground on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 7 m high. Find the width of the street if the length of the ladder is 25 m.

5. There is a field in the shape of a trapezium ABCD. Two perpendiculars are dropped, BE from B to the base CD and AF from A to the base CD. EC : DC = 1 : 3, BE : EC = 1 : 1 and AB : BE = 3 : 2 and BC = 25 m. Find the area of the trapezium in m2.

6. The area of a circle is increased by 44 cm2 when its radius is increased by 2 cm. Find the original radius of the circle in cm.

7. The sum of the radius and height of a cylinder is 35 cm. its total surface area is 1540 cm2. What is the volume of cylinder?

8. The perimeter of a rhombus is 100 cm. If one of the diagonals measures 14 cm, then the area of the rhombus is:

9. The height of an equilateral triangle is 15 cm. Find the area of the triangle.

10. The side of an equilateral triangle whose area is 4√3 cm2 is:

11. One side of the parallelogram is 23 cm. its distance from opposite side is 12 cm. Find the area of parallelogram.

12. The difference between the circumference and the radius of a circle is 111 cm. The area of the circle is

13. How many meters of cloth 5.2 metre wide will be required to make a conical tent, the radius of whose base is 10 m and height is 24 m?

14. A right circular cone and a right cylinder have the same base radius and the same volume. What is the ratio of the heights of the cone to that of the cylinder?

15. Find out the ratio of the volume of a cube and volume of a ball, if the ball fits exactly inside the cube

16. If twice the perimeter of a square is 5.8 cm less than 3 times the sum of its diagonals, then find the side of the square.

17. Length, breadth and height of a room are 10 m, 30 m, and 20 m respectively. Find the volume of the room if each side is increased by 10 %.

18. An equilateral triangle and a regular hexagon have equal perimeters. The ratio of the area of the triangle and that of the hexagon will be

19. A circular ring has an inner radius of 10 cm and outer radius of 20 cm. A point P is taken on its inner boundary and a point Q is taken on its outer boundary such that P, Q and centre of ring are collinear. Another point R is taken on the outer boundary such that PR = 2PQ. With PR as radius, a sphere is formed. What will be the volume of the sphere (in cubic cm)?

20. In a square sheet of side length 10 cm, mid points of two adjacent sides are joined. The sheet is cut along the joined line, so that the remaining piece left is a pentagon. Taking the average of lengths of five sides of this pentagon as radius, a circle is drawn. What is the area of the circle drawn (in square cm)? (Take π = 3.14)

21. A parallelogram with area 90√3 cm2 has adjacent sides of 15 cm and 12 cm. Find the length of its diagonals.

22. A group of kids decided to compete by throwing maximum number of stones in a tank which is 80 m long and 50 m. broad. If 250 stones were thrown by them and the average displacement of 1 stone is 4 cub. m, what was the rise in the water level?

23. If 125 small spherical balls can be made from a large sphere of diameter 40 cm, find the diameter of the small spherical ball.

24. A, B, C is a triangle and D, E, F are the mid-points of the sides BC, CA and AB respectively. The ratio of the areas of ΔABC and ΔDEF is:

25. A circle is drawn with diameter 20 cm. A point P is taken on the circle such that the triangle PQR formed by P with diameter QR is isosceles. What will be the area of minor segment formed by chord PQ (in square cm)?

26. A single solid sphere is melted into three solid spheres of lead whose radii are 1 cm, 6 cm, 8 cm respectively. Find the radius of the original sphere.

27. What is the height of the cylinder if its volume is given by 210 cubic meters and its base area is given by 30 square meters?

28. How many cubes each of surface area of 6 sq. dm. can be made from a metre cube?

29. What is the area of a circle whose radius is equal to the side of a square whose perimeter is 196 metres?

30. A hemisphere, a cylinder and a cone stand on the same base and 45% of height of hemisphere is equal to one - fourth of 180% of height of cylinder and height of cone is one - fourth of sum of 224% of height of hemisphere and 176% of height of cylinder. The ratio of the areas of their curved surface is