The volume of a sphere is 4,000π m3. What is the surface area of the sphere to the nearest square meter? 181 m2 50,265 m2 2,614 m2 1,307 m2
Volume of a sphere = 4/3 πr³
4/3 3.14 r³ = 4000
4.19 r³ = 4000
r³ = 4000 / 4.19
r = ∛1058
r = 10.19
Now, surface area = 4πr² = 4 3.14 (10.19)²
S.A. = 12.56 104
S.A. = 1307
In short, Your Answer would be Option D) 1307 m²
Hope this helps!
Answer:
\(2614\text{ m}^2\)
Step-by-step explanation:
We have been given that the volume of a sphere is \(4,000\pi\text{ m}^3\). We are asked to find the surface area of the sphere.
We will use volume of sphere formula to solve for the radius of sphere as:
\(\text{Volume of sphere}=\frac{4}{3}\pi r^3\)
\(4,000\pi\text{ m}^3=\frac{4}{3}\pi r^3\)
Multiplying both sides by \(\frac{3}{4}\), we will get:
\(\frac{3}{4}*4,000\pi\text{ m}^3=\frac{4}{3}*\frac{3}{4}*\pi r^3\)
\(3,000\pi \text{ m}^3=\pi r^3\)
Now, we will divide both sides of our equation by pi.
\(\frac{3,000\pi\text{ m}^3}{\pi}=\frac{\pi r^3}{\pi}\)
\(3,000\text{ m}^3=r^3\)
Taking cube root of both sides we will get,
\(\sqrt[3]{3,000\text{ m}^3}=r\)
\(10\sqrt[3]{3}\text{ m}=r\)
Now, substituting \(r=10\sqrt[3]{3}\text{ m}\) in surface area of sphere formula, we will get,
\(\text{Surface area of sphere}=4\pi r^2\)
\(\text{Surface area of sphere}=4\pi (10\sqrt[3]{3}\text{ m})^2\)
\(\text{Surface area of sphere}=4\pi*208.0083823051904115\text{ m}^2\)
\(\text{Surface area of sphere}=2613.9104229\text{ m}^2\approx 2614\text{ m}^2\)
Therefore, option D is the correct choice.