Question

the radius, r, of a sphere is 6.6 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: Recall the formula for the volume of a sphere

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi R^{3}\).

Step2: Substitute the given values

Given \( R = 6.6\) mm and \( \pi=3.14\). First, calculate \( R^{3}\): \( R^{3}=(6.6)^{3}=6.6\times6.6\times6.6 = 287.496\). Then, substitute into the formula: \( V=\frac{4}{3}\times3.14\times287.496\).

Step3: Perform the multiplication

\(\frac{4}{3}\times3.14\times287.496 = 4\times3.14\times95.832\) (since \(\frac{287.496}{3}=95.832\)). \(4\times3.14 = 12.56\), and \(12.56\times95.832=1203.65952\).

Step4: Round to the nearest tenth

Rounding \(1203.65952\) to the nearest tenth gives \(1203.7\).

Answer:

\(1203.7\)