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22-03-2020
Mathematics

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A sphere has a radius of r. What is the area of a cross section taken at a distance of 1/2r from the center of the sphere?

A. 1/4r^2
B. 1/2r^2
C. 1/2pie(r)^2
D. 3/4pie(r)^2

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MathPhys MathPhys

22-03-2020

Answer:

D. ¾ πr²

Step-by-step explanation:

If r is the radius of the sphere, and R is the radius of circular cross section, then:

r² = (½ r)² + R²

r² = ¼ r² + R²

¾ r² = R²

So the area of the circular cross section is:

A = πR²

A = ¾ πr²

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