Question

A rectangular pyramid fits exactly on top of a rectangular prism. The prism has length 15 cm, width 5 cm, and height 7 cm, and the pyramid has height 13 cm. Find the volume of the composite space figure.

A) 1500 cm3
B) 500 cm3
C) 2275 cm3
D) 850 cm3

Answer 1

D.
`\text{850 cm}^3`

Step-by-step explanation:

We have been given that a rectangular pyramid fits exactly on top of a rectangular prism. The prism has length 15 cm, width 5 cm, and height 7 cm, and the pyramid has height 13 cm.

The volume of the composite figure will be equal to the volume of rectangular pyramid plus the volume of rectangular prism.

`\text{Volume of composite figure}=\text{Volume of rectangular pyramid+Rectangular prism}`

`\text{Volume of composite figure}=(l*w*h)/(3)+l*w*h`, where,

l = Length,

w = Width,

h = Height

`\text{Volume of composite figure}=(\frac{\text{15 cm*5 cm*13 cm}}{3})+\text{15cm*5cm*7cm}`

`\text{Volume of composite figure}=(\text{5 cm*5 cm*13 cm})+\text{15cm*5cm*7cm}`

`\text{Volume of composite figure}=\text{325 cm}^3+525 cm}^3`

`\text{Volume of composite figure}=\text{850 cm}^3`

Therefore, the volume of composite figure will be 850 cubic cm and option D is the correct choice.