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iren2701 [21]
3 years ago
5

The volume of a sphere is 5,000pi m3. What is the surface area of the sphere to the nearest square meter?

Mathematics
2 answers:
frez [133]3 years ago
6 0

Answer: 1024\pi\ m^2

Step-by-step explanation:

The volume of a sphere is given by :-

\text{Volume}=\dfrac{4}{3}\pi\ r^3, where r is the radius of the sphere.

Given: The volume of a sphere =5,000\pi\ m^3

\Rightarrow5000\pi=\dfrac{4}{3}\pi r^3\\\\\Rightarrow\ r^3=\dfrac{3}{4}\times5000\\\\\Rightarrow\ r^3=3750\\\\\Rightarrow\ r=15.536162\approx16\ m

The surface area of sphere is given by :-

\text{SA}=4\pi r^2\\\\\Rightarrow\text{SA}=4\pi(16)^2\\\\\Rightarrow\ SA=1024\pi\ m^2

tia_tia [17]3 years ago
5 0
Surface area of a sphere = <span>4π<span>r2</span></span>
 the volume of a sphere= <span><span>43</span>π<span>r3</span></span>
 so <span>5000π=<span>4/3</span><span>πr3
</span></span><span>> r^3 = 5000 x 3 / 4 =>
 r^3 = 3750
</span>taking cube root on both sides
r=15.53616
hope it helps
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