Question

the radius, r, of a sphere is 4.2 cm. 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 = □ cm³

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the given values

Given \( R = 4.2\mathrm{cm} \) and \( \pi=3.14 \). First, calculate \( R^{3} \): \( R^{3}=(4.2)^{3}=4.2\times4.2\times4.2 = 74.088 \). Then, substitute into the formula: \( V=\frac{4}{3}\times3.14\times74.088 \).

Step3: Perform the multiplication

\(\frac{4}{3}\times3.14\times74.088=(4\times3.14\times74.088)\div3\). \(4\times3.14 = 12.56\), and \(12.56\times74.088=929.54528\). Then \(929.54528\div3 = 309.848427\).

Step4: Round to the nearest tenth

Rounding \(309.848427\) to the nearest tenth. The digit in the hundredth place is \(4\), so \(309.848427\approx309.8\).

Answer:

\(309.8\)