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What is the volume of a sphere whose surface area is $$100\pi$$ square units? （   ）
A. $$\dfrac{100}{3}\pi$$ cubic units or units3
B. $$\dfrac{500}{3}\pi$$ units3
C. $$160\pi$$ units3
D. $$\dfrac{375}{4}\pi$$ units3
E. $$520$$ units3
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## Gauth Tutor Solution

Helen
University of Nairobi
Algebra teacher
B
Explanation
The formula for the surface area of a sphere is SA $$=4 \pi r^{2}$$.
$$100\pi =4\pi r^{2}$$$$25=r^{2}$$$$5=r$$
The volume is, therefore, $$\dfrac{4}{3} \pi r^{3}=\dfrac{4}{3} \pi (5)^{3}=\dfrac{4}{3} \pi (125)=\dfrac{500}{3} \pi$$.
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