Question

the diameter, d, of a sphere is 17.2 mm. calculate the spheres volume, v. use the value 3.14 for π, and round your answer to the nearest tenth. (do not round any intermediate computations.) v = mm³

Explanation:

Step1: Find the radius

The radius \( r \) of a sphere is half of its diameter \( D \). Given \( D = 17.2 \) mm, so \( r=\frac{D}{2}=\frac{17.2}{2} = 8.6 \) mm.

Step2: Use the volume formula for a sphere

The formula for the volume \( V \) of a sphere is \( V=\frac{4}{3}\pi r^{3} \). We know \( \pi = 3.14 \) and \( r = 8.6 \) mm. Substitute these values into the formula:
\[

$$\begin{align*} V&=\frac{4}{3}\times3.14\times(8.6)^{3}\\ &=\frac{4}{3}\times3.14\times636.056\\ &=\frac{4\times3.14\times636.056}{3}\\ &=\frac{8004.57088}{3}\\ &\approx2668.2 \end{align*}$$

\]

Answer:

\( 2668.2 \)