Question

Two rectangular prisms have the same volume. The area of the base, B, of the blue prism is 418 square units. The area of the base, B, of the red prism is half that of the blue prism. Which statement is true? A rectangular prism with side length h. B = 4 and one-eighth square units. The base of the prism. B = one-half times (4 and one-eighth square units).

Answer 1

The height of the blue prism is half the height of the red prism

Explanation:

Represent the volume of the blue prism with Vb and the red prism with Vr

So, we have:

`V_r = V_b`

`A_b = 418` --- base area of the blue

`A_r = (1)/(2)A_b` --- base area of the red

Required

Determine which statement about the heights of the prisms is true

Volume is calculated as:

`Volume = Base\ Area * Height`

For the blue prism:

`V_b = A_b * h_b`

For the red prism

`V_r = A_r * h_r`

Equate both volumes

`V_r = V_b`

`A_r * h_r = A_b * h_b`

Substitute the expression for
`A_r`

`(1)/(2)A_b * h_r = A_b * h_b`

Divide both sides by
`A_b`

`(1)/(2) h_r = h_b`

This implies that the height of the blue prism is half the height of the red prism