To solve this problem, we need to use the formulas for the volume and surface area of a sphere.
The volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
Given the volume \( V \) is 268.08 cm³, we can solve for the radius \( r \):
\[ 268.08 = \frac{4}{3} \pi r^3 \]
First, solve for \( r^3 \):
\[ r^3 = \frac{268.08 \times 3}{4 \pi} \]
\[ r^3 = \frac{804.24}{4 \pi} \]
Using \( \pi \approx 3.1416 \):
\[ r^3 = \frac{804.24}{12.5664} \]
\[ r^3 = 64 \]
Next, solve for \( r \) by taking the cube root of both sides:
\[ r = \sqrt[3]{64} \]
\[ r = 4 \, \text{cm} \]
The surface area \( A \) of a sphere is given by:
\[ A = 4 \pi r^2 \]
Using \( r = 4 \) cm:
\[ A = 4 \pi (4)^2 \]
\[ A = 4 \pi \times 16 \]
\[ A = 64 \pi \]
Using \( \pi \approx 3.1416 \):
\[ A \approx 64 \times 3.1416 \]
\[ A \approx 201.06 \, \text{cm}^2 \]
So, the surface area of the sphere is \(\boxed{201.06 \, \text{cm}^2}\).
14. If the volume of a sphere is 268.08 cm cubed.
What is the surface area of the sphere?
201.06 cm squared
314.16 cm squared
452.39 cm squared
804.25 cm squared
1 answer