Question

the diameter, d, of a sphere is 9.2 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: Find the radius

The radius \( r \) is half of the diameter \( D \). So \( r=\frac{D}{2}=\frac{9.2}{2} = 4.6 \) cm.

Step2: Use the volume formula for a sphere

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3} \). Substitute \( \pi = 3.14 \) and \( r = 4.6 \) into the formula.
First, calculate \( r^{3} \): \( 4.6^{3}=4.6\times4.6\times4.6 = 97.336 \)
Then, calculate \( \frac{4}{3}\times3.14\times97.336 \)
\( \frac{4}{3}\times3.14 = \frac{12.56}{3}\approx4.1867 \)
Then, \( 4.1867\times97.336\approx407.5 \) (after rounding to the nearest tenth)

Answer:

\( 407.5 \)