Introduction :

In geometry, the term volume refers the space occupied by the three dimensional shapes. Volume is expressed in terms of cubic units. In geometry, the volume can be calculated for all kind of
three dimensional shapes. But the formula to calculate the volume in geometry will vary for each shape. In this article we shall see about formula used to find the volume with example
problems.

Geometry Solving for Volume - Example Problems:

Cube:

Volume of the cube V= a x a x a

V = a3 cubic units

V is the volume of the cube

a is the side length

1. Find the volume of a cube whose side length 23.4 cm.

Solution:

Given:

a = 23.4 cm

Solving for volume:

Formula:

Volume of the cube, V = a3 cubic units

= 23.4 x 23.4 x 23.4

Volume of the cube, V = 12812.904 cm3.

Cuboid:

Volume of the cuboid (v) = l x w x h cubic units.

V=volume

l=length

w=width

h=height

2. Find the volume of the coboid whose length = 8 cm width = 3 cm, height = 6 cm.

Solution:

Given:

Length = 8 cm

Width = 3 cm

Height = 6 cm

Solving for volume:

Formula:

Volume of the cuboids = length x width x height.

= 8 x 3 x 6

= 144 cm3

Sphere:

Formula for Volume of the sphere (v) = 4/3 p r 3 cubic units

V=volume of sphere.

r=radius

3. The radius of the sphere is 10.30 cm. Find the volume of the sphere.

Solution:

Given:

Radius (r) = 10.30 cm

Solving for volume:

Volume of the sphere = `4/3` p r 3 cubic units

= `4/3` x 3.14 x (10.30) 3

= `4/3` x 3.14 x 1092.727

= 4574.88 cm3

Geometry Solving for Volume - more Example Problems:

Cylinder:

Formula for volume of the cylinder (v) = p r2 h cubic units

V=volume of cylinder

r=radius

h=height

4. The cylinder has the radius r= 8 cm, h=17 cm. Find the volume of cylinder.

Solution:

Given:

Solving for volume:

r=8 cm

h=17 cm

Volume of the cylinder = p x r2 x h cubic units

=3.14 x (8)2 x 17

= 3416.32 cm3

Cone:

Formula for volume of the cone (v) =1/3 p r2 h cubic units

V=volume of cone

r=radius

h=height

5. The cone has the radius = 8 cm and height = 17 cm. Find the volume of the cone.

Solution:

Given:

Radius (r) = 8 cm

Height (h) =17 cm

Solving for volume:

Volume of the cone =`1/3` x p x r2 x h cubic units

= `1/3` x 3.14 x (8)2 x 17

= 1138.77 cm3