Question

question 19 of 21
w_{prism} = 30
l_{prism} = 30
h_{prism} = 30
h_{pyramid} = 40
what is the volume of this solid?
a. 27,000
b. 63,000
c. 100,800
d. 39,000

Explanation:

Step1: Volume of the prism (cube)

The prism is a cube with side length \( s = 30 \). Volume of a cube is \( V_{prism}=s^3 \).
\( V_{prism}=30\times30\times30 = 27000 \)

Step2: Volume of the pyramid

The pyramid has a square base with side length \( s = 30 \) and height \( h = 40 \). Volume of a pyramid is \( V_{pyramid}=\frac{1}{3}s^2h \).
\( V_{pyramid}=\frac{1}{3}\times30\times30\times40 = 12000 \)

Step3: Total volume of the solid

Add the volumes of the prism and the pyramid.
\( V_{total}=V_{prism}+V_{pyramid}=27000 + 12000=39000 \)

Answer:

D. 39,000