Find the radius of a sphere having a surface area of 1,018 cm2.

To find the radius of a sphere given its surface area, we use the formula for the surface area of a sphere:

\[
A = 4\pi r^2
\]

Where:
- \( A \) is the surface area,
- \( r \) is the radius.

Given that \( A = 1018 \, \text{cm}^2 \), we can solve for \( r \).

### Step 1: Rearrange the formula to solve for \( r \):
\[
r^2 = \frac{A}{4\pi}
\]
\[
r = \sqrt{\frac{A}{4\pi}}
\]

### Step 2: Substitute the given surface area into the formula:
\[
r = \sqrt{\frac{1018}{4\pi}}
\]

Now, let's calculate the value of \( r \).

\[
r = \sqrt{\frac{1018}{4\pi}} \approx \sqrt{\frac{1018}{12.566}} \approx \sqrt{81.03} \approx 9 \, \text{cm}
\]

So, the radius of the sphere is approximately **9 cm**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would you find the volume of the same sphere?
2. What is the surface area of a sphere with a radius of 12 cm?
3. If the surface area were doubled, how would the radius change?
4. What is the relationship between the radius and volume of a sphere?
5. How does the formula for the surface area of a sphere compare to that of a cylinder?

**Tip:** Always check if units are consistent when solving geometry problems involving area, volume, or length.

Find the radius of a sphere having a surface area of 1,018 cm².

Learn how to find the radius of a sphere with a surface area of 1,018 cm². This step-by-step solution explains the key geometry formulas and concepts involved, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation