Question

Two rectangular prisms have a combined volume of 432 cubic feet. Prism A has half the volume of Prism B.

a. What is the volume of Prism A? Prism B?
b. If Prism A has a base area of 24 ft², what is the height of Prism A?
c. If Prism B’s base is 2/3 the area of Prism A’s base, what is the height of Prism B?

Answer 1

The answer will be b

Answer 2

a. 144 cubic foot

b. 12 ft

c. 18 ft

Explanation:

Let the volume of prism A be V_a

and that of prism b be V_b

ATQ, V_a + V_b= 432

also V_a= 0.5 V_b

⇒1.5 V_b= 432

= V_b= 432/1.5= 288 cubic feet

therefore V_a= 144 cubic feet

volume of prism= area of base×height = V_a

24×h = 144

⇒h= 12 ft

A_b= 2/3×24

⇒base area of prism B= 16 sq.ft

now 16×h_b= 288⇒h_b= 288/16= 18 ft