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

Volume of composite figure = 850 cubic cm.

Explanation:

Given : 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.

To find : Find the volume of the composite space figure.

Solution : We have given that

Prism length 15 cm

Width = 5 cm.

Height = 7 cm.

pyramid height = 13 cm

Width = 5 cm

Length = 15 cm.

Volume of composite space = volume of prism + volume of pyramid .

Volume of composite space = (l* b * h )+(
`(1)/(3) length *width * height` .

Plugging the values of length , width , height

Volume of composite figure = ( 15* 5 *7 ) +( tex]\frac{1}{3} 15 * 5 * 13)[/tex] .

Volume of composite figure = (525 ) +( 325)

Volume of composite figure = 850 cubic cm.

Therefore, Volume of composite figure = 850 cubic cm.

Answer 2

Volume of figure = volume of prism + volume of pyramid
Volume of figure = l x b x h + 1/3 x l x b x h
Volume of figure = 15 x 5 x 7 + 1/3 x 15 x 5 x 13
Volume of figure = 525 + 325 = 850 cm^3