问题1692: The area of the uniform cross section of a prism

Let's solve the problem step by step.

Given:

• Volume of the prism, \( V = 180 \text{cm}^3 \)
• Area of the uniform cross section, \( A = 24 \text{cm}^2 \)

We need to find the height \( h \) of the prism.

The formula for the volume of a prism is:
\[
V = A \times h
\]
where:

• \( V \) is the volume,
• \( A \) is the area of the cross section,
• \( h \) is the height.

We can rearrange this formula to solve for \( h \):
\[
h = \frac{V}{A}
\]

Now, substitute the given values:
\[
h = \frac{180}{24}
\]

Calculate the division:
\[
h = 7.5
\]

Therefore, the height of the prism is \( 7.5 \text{cm} \).

\[
\boxed{7.5}
\]

添加微信可以更快获取解答