Respuesta :
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!
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:
[tex]2614\text{ m}^2[/tex]
Step-by-step explanation:
We have been given that the volume of a sphere is [tex]4,000\pi\text{ m}^3[/tex]. 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:
[tex]\text{Volume of sphere}=\frac{4}{3}\pi r^3[/tex]
[tex]4,000\pi\text{ m}^3=\frac{4}{3}\pi r^3[/tex]
Multiplying both sides by [tex]\frac{3}{4}[/tex], we will get:
[tex]\frac{3}{4}*4,000\pi\text{ m}^3=\frac{4}{3}*\frac{3}{4}*\pi r^3[/tex]
[tex]3,000\pi \text{ m}^3=\pi r^3[/tex]
Now, we will divide both sides of our equation by pi.
[tex]\frac{3,000\pi\text{ m}^3}{\pi}=\frac{\pi r^3}{\pi}[/tex]
[tex]3,000\text{ m}^3=r^3[/tex]
Taking cube root of both sides we will get,
[tex]\sqrt[3]{3,000\text{ m}^3}=r[/tex]
[tex]10\sqrt[3]{3}\text{ m}=r[/tex]
Now, substituting [tex]r=10\sqrt[3]{3}\text{ m}[/tex] in surface area of sphere formula, we will get,
[tex]\text{Surface area of sphere}=4\pi r^2[/tex]
[tex]\text{Surface area of sphere}=4\pi (10\sqrt[3]{3}\text{ m})^2[/tex]
[tex]\text{Surface area of sphere}=4\pi*208.0083823051904115\text{ m}^2[/tex]
[tex]\text{Surface area of sphere}=2613.9104229\text{ m}^2\approx 2614\text{ m}^2[/tex]
Therefore, option D is the correct choice.
