Question

The figure is composed of a rectangular prism and a triangular prism. Find the volume of the figure.

Answer 1

Given:

The given figure is composed of a rectangular prism and a triangular prism.

The length of the rectangular prism is 30 inches.

The width of the rectangular prism is 14 inches.

The height of the rectangular prism is 14 inches.

The base of the triangle is 7 inches.

We need to determine the volume of the composite figure.

Volume of the rectangular prism:

The volume of the rectangular prism can be determined using the formula,

`V=lwh`

Substituting l = 30, w = 14 and h = 14, we get;

`V=30 * 14 * 14`

`V=5880 \ in^3`

Thus, the volume of the rectangular prism is 5880 cubic inches.

Volume of the triangular prism:

The volume of the triangular prism can be determined using the formula,

`V=(1)/(2)bhl`

where b is the base of the triangle,

h is the height of the triangle and

l is the length of the prism.

Substituting b = 7, h = 14 and l = 30, we get;

`V=(1)/(2)(7)(14)(30)`

`V=1470 \ in^3`

Thus, the volume of the triangular prism is 1470 cubic inches.

Volume of the composite figure:

The volume of the composite figure can be determined by adding the volume of the rectangular prism and the volume of the triangular prism.

Thus, we have;

`Volume = 5880+1470`

`Volume = 7350 \ in^3`

Hence, the volume of the composite figure is 7350 cubic inches.