# Volume Worksheet

### Solutions

1Calculate the surface area and the volume of a regular tetrahedron with an edge of 5 cm.

2Calculate the diagonal, lateral area, suface area and volume of a cube with an edge of 5 cm.

3Calculate the surface area and the volume of a regular octahedron with an edge of 5 cm.

4Calculate the suface area and volume of a dodecahedron with an edge of 10 cm, knowing that the apothem of one face measures 6.88 cm.

5Calculate the surface area and the volume of a regular icosahedron with an edge of 5 cm.

6Calculate the lateral area, surface area and volume of a prism whose base is a rhombus with diagonals of 12 and 18 cm in length.

7Calculate the lateral area, surface area and volume of a square pyramid whose base edge is 10 cm and its height is 12 cm.

8Calculate the lateral area, surface area and volume of a hexagonal pyramid with a base edge of 16 cm and a side edge of 28 cm.

9Calculate the lateral area, suface area and volume of a truncated square pyramid whose base edges are 24 and 14 cm and whose lateral edge is 13 cm.

10Calculate the lateral area, surface area and volume of a cone whose slant height is 13 cm and base radius is 5 cm.

11Calculate the lateral area, surface area and volume of a cone whose height is 4 cm and base radius is 3 cm.

12Calculate the lateral area, surface area and volume of a truncated cone with radii of 2 and 6 cm and a height of 10 cm.

13Calculate the lateral area, surface area and volume of a truncated cone with radii of 12 and 10 cm and a slant height of 15 cm.

14Calculate the area of the circle resulting from cutting a sphere with a 35 cm radius by a plane whose distance from the center of the sphere is 21 cm.

15Calculate the area and volume of a sphere inscribed in a cylinder with a height of 2 m.

16Calculate the volume of a hemisphere with a radius of 10 cm.

17Calculate the area and volume of the following spherical cap.

18Calculate the area of the spherical zone and the volume of a spherical segment whose radius circles are 10 and 8 cm and the distance between them is 5 cm.

## 4

Calculate the suface area and volume of a dodecahedron with an edge of 10 cm, knowing that the apothem of one face measures 6.88 cm.

## 6

Calculate the lateral area, surface area and volume of a prism whose base is a rhombus with diagonals of 12 and 18 cm in length.

## 7

Calculate the lateral area, surface area and volume of a square pyramid whose base edge is 10 cm and its height is 12 cm.

## 8

Calculate the lateral area, surface area and volume of a hexagonal pyramid with a base edge of 16 cm and a side edge of 28 cm.

## 9

Calculate the lateral area, suface area and volume of a truncated square pyramid whose base edges are 24 and 14 cm and whose lateral edge is 13 cm.

## 10

Calculate the lateral area, surface area and volume of a cone whose slant height is 13 cm and base radius is 5 cm.

## 11

Calculate the lateral area, surface area and volume of a cone whose height is 4 cm and base radius is 3 cm.

## 12

Calculate the lateral area, surface area and volume of a truncated cone with radii of 2 and 6 cm and a height of 10 cm.

## 13

Calculate the lateral area, surface area and volume of a truncated cone with radii of 12 and 10 cm and a slant height of 15 cm.

## 14

Calculate the area of the circle resulting from cutting a sphere with a 35 cm radius by a plane whose distance from the center of the sphere is 21 cm.

## 18

Calculate the area of the spherical zone and the volume of a spherical segment whose radius circles are 10 and 8 cm and the distance between them is 5 cm.