Question

find the surface area and volume of the solid. round each measure to the nearest tenth, if necessary.
a) surface area = 12.95π or about 40.1 cm²
volume = 7.775π or about 24.8 cm³
b) surface area = 12.96π or about 40.7 cm²
volume = 7.776π or about 24.4 cm³
c) surface area = 42.7 cm²
volume = 25 cm³
d) surface area = 11.2π or about 35.1 cm²
volume = 6.576π or about 20.65 cm³

Explanation:

Step1: Recall Sphere Formulas

The surface area \( S \) of a sphere is \( S = 4\pi r^2 \), and the volume \( V \) is \( V=\frac{4}{3}\pi r^3 \), where \( r = 1.8 \, \text{cm} \).

Step2: Calculate Surface Area

Substitute \( r = 1.8 \) into the surface area formula:
\( S = 4\pi(1.8)^2 = 4\pi(3.24)=12.96\pi \approx 12.96\times3.1416\approx40.7 \, \text{cm}^2 \).

Step3: Calculate Volume

Substitute \( r = 1.8 \) into the volume formula:
\( V=\frac{4}{3}\pi(1.8)^3=\frac{4}{3}\pi(5.832)=7.776\pi \approx 7.776\times3.1416\approx24.4 \, \text{cm}^3 \).

Answer:

B) Surface area \( = 12.96\pi \) or about \( 40.7 \, \text{cm}^2 \), Volume \( = 7.776\pi \) or about \( 24.4 \, \text{cm}^3 \)