Question

q13. determine the surface area and the volume of a sphere with a radius of 5 cm.

Explanation:

Step1: Recall formulas for sphere

Surface area of sphere: \( SA = 4\pi r^2 \)
Volume of sphere: \( V=\frac{4}{3}\pi r^3 \)
Given \( r = 5\space cm \)

Step2: Calculate Surface Area

Substitute \( r = 5 \) into \( SA = 4\pi r^2 \)
\( SA = 4\pi(5)^2 = 4\pi\times25 = 100\pi \approx 314\space cm^2 \)

Step3: Calculate Volume

Substitute \( r = 5 \) into \( V=\frac{4}{3}\pi r^3 \)
\( V=\frac{4}{3}\pi(5)^3=\frac{4}{3}\pi\times125=\frac{500}{3}\pi\approx 523.6\space cm^3 \)

Answer:

Surface Area: \( 100\pi\space cm^2 \) (or approximately \( 314\space cm^2 \))
Volume: \( \frac{500}{3}\pi\space cm^3 \) (or approximately \( 523.6\space cm^3 \))