Question

quiz 5.3.1 - volumes of prisms and cylinders
find the volume of the prism.
a. 152 km³
b. 216 km³
c. 109 km³
d. 113 km³
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Explanation:

Step1: Recall volume formula for prism

$V = Bh$, where $B$ is base - area and $h$ is height. For a triangular - based prism, if the base is a right - triangle with legs $a = 6$ km and $b = 8$ km, the area of the base $B=\frac{1}{2}ab$.
$B=\frac{1}{2}\times6\times8= 24$ km²

Step2: Identify height of prism

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

Step3: Calculate volume of prism

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

Answer:

B. 216 km³