# Worksheet on Volume of a Pyramid

Math worksheet on volume of a pyramid will help us to practice the different questions for finding volume of a pyramid.

1. The base of a right pyramid 10 √7 feet high is a triangle whose sides are 9 feet, 11feet and 16 feet. Find the volume of the pyramid.

2. The base of right pyramid is a triangle whose sides are 28 cm, 25cm and 17 cm. If the volume of the pyramid be 11120 cubic cm, find its height.

3. The base of a right pyramid is a square of 40 cm and its slant height is 25 cm. If the value of cube is equal to the volume of the pyramid find the length of a side of the cube.

4. The base of a right pyramid is a square of side 40 cm and length of an edge through the vertex is 5√41 cm. If the volume of a cube is equal to the volume of the pyramid, then find length of the side of the cube.

5. The base of a right pyramid is a square of side 12 cm. If its slant height is 6√5 cm, find its volume.

6. The base of a right pyramid is a rectangle whose length and breadth are 18 cm and 15 cm respectively. If its height be 24 cm, find its volume.

7. The base of a right pyramid is a rectangle whose length and breadth are 24 cm and 18 cm respectively. If its length of its slant edge is 17 cm, find the height and volume of the pyramid.

8. The base of a right pyramid, 5√3 cm height, is a regular hexagon of side 6 cm. Find its volume.

9. OA, OB, OC are there mutually perpendicular straight lines in space. If OA = a, OB = b, and OC = c, prove that the volume of the pyramid OABC is (1/6) abc.

10. The base of a right pyramid 15 cm height cm is a regular octagon. If the volume of the pyramid 160(√2 + 1) cubic cm, find the length of a side of the octagon.

11. The base of a right pyramid is a square of side 12 cm and the dihedral angle between its base and a lateral face is 60°. Find its height and volume.

12. The base of right pyramid, 15 cm. High, is a square of side 16 cm. Its upper part is cut off by a plane parallel to the base and through the middle of its height. Find the volume of the frustum of the pyramid formed.

13. The lower and upper faces of the frustum of a right pyramid are squares of sides 16 cm and 9 cm respectively. If the height of the pyramid be 12 cm, then find its volume.

14. The upper and lower faces of the frustum of a right pyramid are a regular of hexagons of sides 8 cm and 12 cm respectively. If the height of the frustum be 2√3 cm, find its volume.

15. The base of right pyramid, h cm height is a square. It is divided into two parts by a plane parallel to the base so that volumes of the two parts are equal. Show that the distance of the plane form the vertex is h/(3√2) cm.

Answers for the worksheet on volume of a pyramid are given below to check the exact answers of the above questions.

1. 420 cu. ft.

2. 16 cm.

3. 20 cm.

4. 20 cm.

5. 576 cu. cm.

6. 2160 cu. cm.

7. 8 cm and 1152 cu. cm.

8. 270 cu. cm.

10. 4 cm.

11. 6√3 cm. and 72√3 cu. cm.

12. 1120 cu. cm.

13. 1924 cu. cm.

14. 2736 cu. cm.

Mensuration