Question

1. -/3 points the diameter of a sphere is measured to be 5.57 in. (a) find the radius of the sphere in centimeters. cm (b) find the surface area of the sphere in square centimeters. cm² (c) find the volume of the sphere in cubic centimeters. cm³

Explanation:

Part (a)

Step 1: Convert diameter to radius (in inches)

The radius \( r \) of a sphere is half of its diameter \( d \). Given \( d = 5.57 \) in, so \( r=\frac{d}{2}=\frac{5.57}{2}=2.785 \) in.

Step 2: Convert inches to centimeters

We know that \( 1 \) inch \( = 2.54 \) cm. So, \( r = 2.785\times2.54 \) cm.
Calculate \( 2.785\times2.54 = 7.0739 \) cm (approx).

Step 1: Recall the formula for the surface area of a sphere

The formula for the surface area \( A \) of a sphere is \( A = 4\pi r^{2} \), where \( r \) is the radius.

Step 2: Substitute the radius value

We found \( r\approx7.0739 \) cm. So, \( A = 4\pi(7.0739)^{2} \).
First, calculate \( (7.0739)^{2}\approx49.939 \). Then, \( 4\pi\times49.939\approx4\times3.1416\times49.939\approx627.1 \) \( \text{cm}^2 \) (approx).

Step 1: 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.

Step 2: Substitute the radius value

We have \( r\approx7.0739 \) cm. So, \( V = \frac{4}{3}\pi(7.0739)^{3} \).
First, calculate \( (7.0739)^{3}\approx7.0739\times7.0739\times7.0739\approx356.0 \) (approx). Then, \( \frac{4}{3}\pi\times356.0\approx\frac{4}{3}\times3.1416\times356.0\approx1490. \) \( \text{cm}^3 \) (approx).

Answer:

\( 7.07 \) (rounded to two decimal places)

Part (b)