Question

question 10 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 the area of the circle

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(r = 12\), we have \(A=\pi\times(12)^{2}=144\pi\).

Step2: Calculate the surface area of the sphere

The formula for the surface area of a sphere is \(S = 4\pi R^{2}\). Given \(R = 6\), we have \(S=4\pi\times(6)^{2}=4\pi\times36 = 144\pi\).
Since the area of the circle (\(144\pi\)) is equal to the surface area of the sphere (\(144\pi\)), the statement is True.

Answer:

A. True