SOLUTION: The area of a cross section of a sphere is 64\% of the largest possible cross sectional area of the sphere. If the sphere has radius 1/2, what is the area of the cross section?

Question 1210141: The area of a cross section of a sphere is 64\% of the largest possible cross sectional area of the sphere. If the sphere has radius 1/2, what is the area of the cross section?

Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let the sphere have radius $r$.
The largest possible cross-sectional area of the sphere is a circle with radius $r$, so its area is $\pi r^2$.
Given that the radius of the sphere is $r = \frac{1}{2}$, the largest possible cross-sectional area is $\pi (\frac{1}{2})^2 = \frac{\pi}{4}$.
The area of the cross section is 64\% of the largest possible cross-sectional area.
Therefore, the area of the cross section is $0.64 \cdot \frac{\pi}{4}$.
$$ 0.64 \cdot \frac{\pi}{4} = \frac{64}{100} \cdot \frac{\pi}{4} = \frac{16}{25} \cdot \frac{\pi}{4} = \frac{4\pi}{25} $$
Thus, the area of the cross section is $\frac{4\pi}{25}$.
Final Answer: The final answer is $\boxed{\frac{4 \pi}{25}}$

Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.
The area of a cross section of a sphere is 64% of the largest possible cross sectional area of the sphere.
If the sphere has radius 1/2, what is the area of the cross section?
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The largest possible cross section area of the given sphere is = = square units. The area of the 64% cross section of the sphere is 0.64 of { {{pi/4}}}, or = = 0.16*3.14159265 = 0.502654824 (approximately). ANSWER. The area of the cross section under the question is = 0.502654824 square units (approximately). You may round it as you want.

Solved.

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