Question

calculate the volume of prism.
$v_{prism} = \boxed{250} \\ cm^3 \\ \\ 250 = 250$
part 2 of 3
calculate the volume of the pyramid.
$v_{pyramid} = \boxed{} \\ cm^3$

Explanation:

Step1: Find the base area of the pyramid

The base of the pyramid is the same as the base of the prism. The prism has a length of 5 cm and (from the prism volume \( V_{prism}=250 \, cm^3 \) and height \( 10 \, cm \), we can find the width? Wait, actually, the prism is a rectangular prism, so \( V_{prism}=l\times w\times h \). We know \( V_{prism}=250 \), \( h = 10 \), \( l = 5 \), so \( 250=5\times w\times 10 \), but actually, maybe the base of the pyramid is a rectangle with length 5 cm and the same width as the prism's base. Alternatively, since the prism's volume is \( 250 = 5\times w\times 10 \), so \( w = 5 \) (since \( 5\times5\times10 = 250 \)). So the base of the pyramid is a square? Wait, no, the prism: length 5, height 10, volume 250, so base area \( B=\frac{V_{prism}}{h_{prism}}=\frac{250}{10}=25 \, cm^2 \). So the base area of the pyramid \( B = 25 \, cm^2 \).

Step2: Find the height of the pyramid

The total height of the figure is 28 cm, and the prism's height is 10 cm, so the pyramid's height \( h_{pyramid}=28 - 10 = 18 \, cm \).

Step3: Calculate the volume of the pyramid

The formula for the volume of a pyramid is \( V_{pyramid}=\frac{1}{3}Bh \), where \( B \) is the base area and \( h \) is the height. We have \( B = 25 \, cm^2 \), \( h = 18 \, cm \). So \( V_{pyramid}=\frac{1}{3}\times25\times18 \).

Step4: Compute the value

\( \frac{1}{3}\times25\times18 = 25\times6 = 150 \, cm^3 \). Wait, wait, no: \( 18\div3 = 6 \), so \( 25\times6 = 150 \). Wait, but let's check again. The base area of the pyramid: the prism has base area \( B = 5\times5 = 25 \) (since \( 5\times5\times10 = 250 \)). The height of the pyramid is total height (28) minus prism height (10), so \( 28 - 10 = 18 \, cm \). Then volume of pyramid is \( \frac{1}{3}\times25\times18 = 150 \, cm^3 \).

Answer:

\( 150 \)