Chapters

## Exercise 1

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

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Jamie
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Matthew
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## Exercise 2

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

## Exercise 3

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

## Exercise 4

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

## Exercise 5

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

## Exercise 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.

## Exercise 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.

## Exercise 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.

## Exercise 9

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

## Exercise 10

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

## Exercise 11

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

## Exercise 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.

## Exercise 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.

## Exercise 14

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

## Exercise 15

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

## Exercise 16

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

## Exercise 17

Calculate the area and volume of the following spherical cap.

## Exercise 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 6 cm.

## Solution of exercise 1

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

## Solution of exercise 2

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

## Solution of exercise 3

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

## Solution of exercise 4

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

## Solution of exercise 5

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

## Solution of exercise 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.

## Solution of exercise 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.

## Solution of exercise 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.

## Solution of exercise 9

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

## Solution of exercise 10

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

## Solution of exercise 11

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

## Solution of exercise 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.

## Solution of exercise 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.

## Solution of exercise 14

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

## Solution of exercise 15

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

## Solution of exercise 16

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

## Solution of exercise 17

Calculate the area and volume of the following spherical cap.

## Solution of exercise 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 6 cm.

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