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?

a. 144 cubic foot

b. 12 ft

c. 18 ft

Step-by-step 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

The answer will be b