Question

mackenzie knows the surface area of a sphere. which explains how she can find the surface area of a hemisphere with the same radius?

divide the surface area of the sphere by 2, and add the area of the base of the hemisphere
multiply the surface area of the sphere by 2, and add the area of the base of the hemisphere
divide the volume of the sphere by 2
multiply the volume of the sphere by 2

Explanation:

Express the surface area of a sphere

$$ A_{\text{sphere}} = 4\pi r^2 $$

Express the surface area of a hemisphere

$$ A_{\text{hemisphere}} = A_{\text{curved}} + A_{\text{base}} = \frac{A_{\text{sphere}}}{2} + \pi r^2 $$

Match with the given options

$$ \text{Hemisphere Surface Area} = \frac{\text{Surface Area of Sphere}}{2} + \text{Area of the Base} $$

Answer:

• (A) Divide the surface area of the sphere by 2, and add the area of the base of the hemisphere (Correct answer)
• (B) Multiply the surface area of the sphere by 2, and add the area of the base of the hemisphere
• (C) Divide the volume of the sphere by 2
• (D) Multiply the volume of the sphere by 2