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olga55 [171]
3 years ago
15

The area of a cross section through the center of a sphere is 46 square inches. Find the surface area of the sphere.

Mathematics
1 answer:
gavmur [86]3 years ago
7 0

Answer:

184 in.^2

Step-by-step explanation:

The cross section through the center of a sphere is a circle whose radius is equal to the radius of the sphere.

area of circle

A_{circle} = \pi r^2

\pi r^2 = 46

r^2 = \dfrac{46}{\pi}

r = \sqrt{\dfrac{46}{\pi}}

r = 3.83 ~in.

surface area of sphere

SA = 4 \pi r^2

SA = 4 \times \pi \times (3.83)^2

SA = 184~in.^2

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