Question

question 1 of 10 the area of a circle of radius 12 units is equal to the surface area of a sphere of radius 6 units. a. true b. false

Explanation:

Step1: Calculate circle area

The formula for the area of a circle is $A_{circle}=\pi r_{1}^{2}$. Given $r_{1} = 12$, then $A_{circle}=\pi\times12^{2}=144\pi$.

Step2: Calculate sphere surface - area

The formula for the surface - area of a sphere is $A_{sphere}=4\pi r_{2}^{2}$. Given $r_{2}=6$, then $A_{sphere}=4\pi\times6^{2}=4\pi\times36 = 144\pi$.

Step3: Compare areas

Since $A_{circle}=144\pi$ and $A_{sphere}=144\pi$, the area of the circle of radius 12 units is equal to the surface area of the sphere of radius 6 units.

Answer:

A. True