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BlueSky06
To get the surface area of the sphere, we need to know the radius. Since the volume is given, we can get the radius.
Volume =  [tex] \frac{4}{3} [/tex]π r³
5000πm³ = [tex] \frac{4}{3} [/tex] π r³
5000m³ = [tex] \frac{4}{3} [/tex] r³
5000m³ x 3 = 4r³
[tex] \frac{15000m³}{4} [/tex] = [tex] \frac{4r³}{4} [/tex]
∛3750 = ∛r³

r = 15.536m
r = 15.54m
Since the radius is now known, substitute it directly to the surface area formula
A = 4π x r²
A = 4π x (15.54)²
A= 3,034.67 m² or 3,035 m²

A sphere is characterized by its radius. The surface area of the specified sphere is [tex]964.7\pi \: \rm meters^2\\[/tex]

What is the volume of sphere?

If the given sphere is of radius r units, then its volume is given as:

[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]

What is the surface area of sphere?

If the given sphere is of radius r units, then its surface area is given as:

[tex]S= 4\pi r^2 \: \rm unit^2[/tex]

For the given case, its given that:

V = 5,000π cubic meters.

Consider the radius of the sphere in consideration be r meters.

Then, we get, from the formula for the volume of sphere as:

[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3\\\\\\5000\pi = \dfrac{4}{3}\pi r^3\\\\\text{Multiplying both sides by }3/4\pi\\\\\dfrac{5000\pi \times 3}{4 \times \pi} = r^3\\\\r^3 = 3750\\\\\text{Taking cube root of both the sides}\\\\r = \:^3\sqrt{3750} \approx 15.53 \: \rm meters[/tex]

Thus, using that radius to find the surface area of the same sphere:

[tex]S= 4\pi r^2 \: \rm unit^2\\\\S = 4\pi (15.53)^2 \approx 964.7 \pi \: \rm meter^2[/tex]

Thus,  The surface area of the specified sphere is [tex]964.7\pi \: \rm meters^2\\[/tex]

Learn more about surface area of sphere here:

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