Question

find the volume of the prism.
a. 152 km³
b. 216 km³
c. 109 km³
d. 113 km³

Explanation:

Step1: Recall volume formula for prism

$V = Bh$, where $B$ is the base - area and $h$ is the height. The base is a right - triangle with legs $a = 6$ km and $b = 8$ km.

Step2: Calculate the base - area

The area of a right - triangle $B=\frac{1}{2}ab$. Substituting $a = 6$ km and $b = 8$ km, we get $B=\frac{1}{2}\times6\times8=24$ km².

Step3: Determine the height of the prism

The height of the prism $h = 9$ km.

Step4: Calculate the volume of the prism

Using the volume formula $V = Bh$, substitute $B = 24$ km² and $h = 9$ km. So $V=24\times9 = 216$ km³.

Answer:

b. $216$ km³