Question

a cone has a diameter of 17 miles and a height of 3.42 miles. which measurement is closest to the volume of the cone in cubic miles?
1,035 $mi^3$
259 $mi^3$
208 $mi^3$
776 $mi^3$

Explanation:

Step1: Find the cone's radius

Radius $r = \frac{\text{diameter}}{2} = \frac{17}{2} = 8.5$ miles

Step2: Recall cone volume formula

Volume formula: $V = \frac{1}{3}\pi r^2 h$

Step3: Substitute values into formula

$V = \frac{1}{3} \times \pi \times (8.5)^2 \times 3.42$
First calculate $(8.5)^2 = 72.25$, then:
$V = \frac{1}{3} \times \pi \times 72.25 \times 3.42$
$\frac{1}{3} \times 3.42 = 1.14$, so:
$V = 1.14 \times 72.25 \times \pi$
$1.14 \times 72.25 = 82.365$
$V = 82.365 \times \pi \approx 82.365 \times 3.1416 \approx 258.7$

Step4: Match to closest value

258.7 is closest to 259.

Answer:

259 $mi^3$