Question

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

Answer 1

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.

Answer 2

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!