Question

last question!! what is the volume of this sphere? round to nearest tenth. 10 in v=418.8in³ v=4189.7in³ v=4189in³ v=417.7in³

Explanation:

Step1: Identify radius

The diameter is 10 in, so radius $r = 5$ in.

Step2: Use volume formula

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = 5$ into the formula: $V=\frac{4}{3}\pi(5)^{3}=\frac{4}{3}\pi\times125=\frac{500\pi}{3}$.

Step3: Calculate and round

$V=\frac{500\pi}{3}\approx\frac{500\times3.14159}{3}\approx523.6$ in³. But if we assume the 10 in is the radius:
$V=\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi(10)^{3}=\frac{4000\pi}{3}\approx\frac{4000\times3.14159}{3}\approx4188.8$ in³, rounding to nearest tenth gives $V = 4188.8$ in³ which is closest to $V = 4189.7$ in³ among the options.

Answer:

D. $V = 4189.7$ in³