Question

A rectangular prism has a base area of 15 cm2
, and pyramid with a congruent base and height has a volume of 20 cm3
. What is the height of the rectangular prism?(1 point)
Responses

43 cm
Start Fraction 4 over 3 End Fraction cm

5 cm
5 cm

4 cm
4 cm

20 cm

Answer 1

To find the height of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is given by:

\[
V = \text{Base Area} \times \text{Height}
\]

We know the base area is \( 15 \, \text{cm}^2 \). Let \( h \) be the height of the rectangular prism. Therefore, we can write the equation for the volume of the prism as:

\[
V_{\text{prism}} = 15 \, \text{cm}^2 \times h
\]

The volume of the pyramid is given as \( 20 \, \text{cm}^3 \). The volume of a pyramid is calculated using the formula:

\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

Since the base area of the pyramid is congruent to the prism's base area, we have:

\[
V_{\text{pyramid}} = \frac{1}{3} \times 15 \, \text{cm}^2 \times h
\]

Setting \( V_{\text{pyramid}} \) to \( 20 \, \text{cm}^3 \):

\[
20 = \frac{1}{3} \times 15 \times h
\]

Now, multiply both sides by 3:

\[
60 = 15 \times h
\]

Next, divide both sides by 15 to solve for \( h \):

\[
h = \frac{60}{15} = 4 \, \text{cm}
\]

Thus, the height of the rectangular prism is:

\[
\boxed{4 \, \text{cm}}
\]