Question

the radius, r, of a sphere is 6.2 m. calculate the sphere’s volume, v. use the value 3.14 for π, and round your answer to the nearest tenth. (do not round any intermediate computations.)

Explanation:

Step1: Recall the volume formula for 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 into the formula

We are given that \( R = 6.2 \, \text{m} \) and \( \pi = 3.14 \). Substituting these values into the formula, we get:

$$ V=\frac{4}{3}\times3.14\times(6.2)^{3} $$

First, calculate \( (6.2)^{3} \):
\( 6.2\times6.2 = 38.44 \), then \( 38.44\times6.2 = 238.328 \)
Now, substitute \( (6.2)^{3}=238.328 \) back into the volume formula:

$$ V=\frac{4}{3}\times3.14\times238.328 $$

Calculate \( \frac{4}{3}\times3.14 \) first: \( \frac{4\times3.14}{3}=\frac{12.56}{3}\approx4.1867 \)
Then multiply this by \( 238.328 \): \( 4.1867\times238.328\approx998.3 \) (after rounding to the nearest tenth)

Answer:

\( 998.3 \)