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

Answer 1

Answer:

Volume of composite space = 850cm³

Step-by-step explanation:

For Prism,

Length l = 15 cm

Width w = 5 cm

Height Hpr = 7 cm

As Rectangular pyramid fits exactlyon top of the prism, length and width of prism is same for the base of the pyramid.

for Prism

Length l =15cm

width w = 5cm

height Hpy = 13 cm

Volume of compoite space = Volume of prism + Volume of Pyramid

Volume of Prism Vpr = l × w × h

∴ Vpr =  15 × 5 × 7

∴ Vpr = 525 cm³   ....(1)

Volume of rectangular Pyramid Vpy = (l×w×h) / 3

∴ Vpy = (15 × 5 × 13) ÷ 3

∴ Vpy = 325 cm³  ....(2)

From 1 and 2, Volume of composite space,

V = Vpr + Vpy

∴ V = 525 + 325 = 850

∴ V = 850 cm³