Volume Worksheet

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.

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.

1

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

Volume Exercise

Volume Solution


2

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

Diagonal of a Cube

Volume Exercise

Volume Operations

Volume Operations

Volume Operations

Volume Solution


3

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

Volume Exercise

Volume Solution


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.

Volume Exercise

Volume Solution


5

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

Volume Exercise

Volume Solution


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.

Prism with Rhombus Base

Volume Exercise

Volume Operations

Volume Operations

Volume Operations

Volume Solution


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.

Square Pyramid


Volume Exercise

Volume Operations

Volume Operations

Volume Operations

Volume Operations

Volume Solution


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.

Hexagonal Pyramid


Volume Exercise

Volume Operations

Volume Solution


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.

tronco de pirámide cuadrangular

solución

solución

solución

solución

solución

solución

solución

solución

solución

solución


10

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


cono


Volume Exercise

Volume Operations

Volume Operations

Volume Operations

Volume Solution


11

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

Cone


Volume Exercise

Volume Operations

Volume Operations

Volume Operations

Volume Solution


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.

Truncated Cone

Volume Exercise

Volume Operations

Volume Operations

Volume Operations

Volume Solution


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.

Truncated Cone

Volume Exercise

Volume Operations

Volume Operations

Volume Operations

Volume Solution


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.

 

Area of a Circle from Cutting a Sphere



Volume Exercise

Volume Solution


15

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

Sphere Inscribed in a Cylinder



Volume Exercise

Volume Solution


16

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

Volume Exercise


17

Calculate the area and volume of the following spherical cap.

Spherical Cap

Volume Exercise

Volume 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 5 cm.

Spherical Segment

Volume Exercise

Volume Solution




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