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**

**Formulas for 3D Shapes****Volume and Surface Area of the Prism****Worksheet on Volume and Surface Area of Prism****Volume and Whole Surface Area of Right Pyramid****Volume and Whole Surface Area of Tetrahedron****Volume of a Pyramid****Volume and Surface Area of a Pyramid****Problems on Pyramid****Worksheet on Volume and Surface Area of a Pyramid****Worksheet on Volume of a Pyramid**

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