Question

1. sphere

a spherical sports ball has a radius of 7 cm.
a. find the surface area.
b. find the volume.

Explanation:

Step1: Surface area formula

The formula for the surface area of a sphere is \(S = 4\pi r^{2}\). Given \(r = 7\mathrm{cm}\), substitute \(r\) into the formula: \(S=4\pi\times(7)^{2}\).

Step2: Calculate surface area

\(S = 4\pi\times49=196\pi\mathrm{cm}^{2}\approx196\times 3.14 = 615.44\mathrm{cm}^{2}\)

Step3: Volume formula

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Substitute \(r = 7\mathrm{cm}\) into the formula: \(V=\frac{4}{3}\pi\times(7)^{3}\).

Step4: Calculate volume

\(V=\frac{4}{3}\pi\times343=\frac{1372}{3}\pi\mathrm{cm}^{3}\approx\frac{1372}{3}\times3.14\approx1436.03\mathrm{cm}^{3}\)

Answer:

a. The surface area is approximately \(615.44\mathrm{cm}^{2}\).
b. The volume is approximately \(1436.03\mathrm{cm}^{3}\).