Question

Two rectangular prisms have the same volume. the area of the base of the blue prism is 2 1/6 square units. The area of the base of the red prism is one third that of the blue prism. Which koo statement is true?

Answer 1

This shows that the height of the red prism will be three times that of blue

Explanation:

Volume of a prism = 1/3 * base area * height

V = 1/3Bh

Vr = 1/3Brhr...1

Vb = 1/3Bbhb... 2

Let the volume of red prism be Vr and the volume of blue prism be Vb. If both prisms have the same volume then Vr = Vb = V.

Also if the area of the base of the red prism is one third that of the blue prism, the B, then Br = 1/3 Bb where Bb = 3Br..(3)

Since the volume are the same then;

1/3Brhr = 1/3Bbhb

Substituting equation 3 intio the resulting expression;

1/3Brhr = 1/3(3Br)hb

hr = 3hb

This shows that the height of the red prism will be three times that of blue