# Worksheet on Volume and Surface Area of a Pyramid

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

1. The base of a right pyramid 12 meter high is an equilateral triangle of side 10√3 meter. Find the volume and slant surface of the pyramid.

2. The length of the edge of a regular tetrahedron is l cm. Find its volume and total lateral surface area.

3. The length of the edge of a regular tetrahedron is 6√6 units. Show that the numerical values of its total surface area and volume are equal.

4. A right pyramid stands on a base 16 cm² and its height is 15 cm find its (a) Slant surface

(b) Whole surface and

(c) Volume.

5. The base of a right pyramid is a square of area 1600 square cm and the volume of this pyramid is 8000 cubic cm. Find the height, length of the sides-edge and area of a side face of the pyramid.

6. The base of a pyramid 16 cm high is a square whose each side is of length 24 cm. Find the slant height and length of slant edge of the pyramid.

7. The base of a right pyramid is a square of side 20 cm. If its side-faces are equilateral triangles, find its volume and the area of whole surface.

8. The base of a right pyramid is a rectangle whose length and breadth are 8 m and 6 m respectively. If its length of its slant edge is 13 m, find its volume and area of side-faces.

9. A right pyramid 8 feet height stands on a rectangular base of area 42 square feet. If the length of each slant edge be 17 feet find the length and breadth of the rectangular base.

10. The base of a right pyramid is a hexagon. If its height is 10 cm and volume 180√3 cubic cm. Find the length of each side of its base. What is the area of total slant surface of the pyramid?

11. The base of a right pyramid is a regular hexagon of area 54√3 square units. If the area of a side-face of the pyramid 9√6 square units, find its volume.

12. The height of a regular tetrahedron is 4√6. Find the volume and whole surface of the tetrahedron.

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

1. 300√3 cu. cm. and 195√3 sq. cm.

2. √2/12 l³ cu. cm. and √3 l² sq. cm.

4. (a) 544 sq. cm. (b) 800 sq. cm. (c) 1280 cu. cm.

5. 5 cm, 5√41 cm. and 500 sq. cm.

6. 20 cm. and 4√34 cm.

7. 1885.3 cu. cm. (approx) and 1092.8 sq. cm. (approx)

8. 192 cu. m. and 24(√17 + √10) sq. m.

9. Length = 24 ft and breadth = 18 ft.

10. 6 cm. and 18√127 sq. cm.

11. 162 cu. units.

12. 144√2 cu. cm. and 144√3 sq. cm.

Mensuration