Surface Area of a Sphere Calculator

Published on: August 4, 2024

Final Answer: Free • Full Steps: Plus

This Surface Area of a Sphere Calculator helps you find the total outer area of a sphere when the radius is known. It uses the formula SA = 4πr², where r is the radius and the answer is written in square units. First square the radius, then multiply by 4π to get the surface area. It is a simple way to check answers, understand the sphere surface area formula, and practise basic geometry step by step.

Radius is labeled r.

Step-by-step method

Identify what is given.
Write the formula.
Substitute the value and calculate the surface area.

Formula:

\(SA = 4\pi r^{2}\)

Example 1:

\(r = 5\)

Step 1 - Identify what is given.

In this problem: The given radius is \(r = 5\).

\(r = 5\)

Step 2 - Write the formula.

In this problem: Use the sphere surface area formula: \(SA = 4\pi r^{2}\).

\(SA = 4\pi r^{2}\)

Step 3 - Substitute the value and calculate the surface area.

In this problem: Substitute \(r = 5\): \(SA = 4\pi \times 5^{2} \approx 314.16\).

\(SA = 4\pi \times 5^{2} \approx 314.16\)

Final answer:

\(SA \approx 314.16\)

Example 2:

\(r = 3.5\)

Step 1 - Identify what is given.

In this problem: The given radius is \(r = 3.5\).

\(r = 3.5\)

Step 2 - Write the formula.

In this problem: Use the sphere surface area formula: \(SA = 4\pi r^{2}\).

\(SA = 4\pi r^{2}\)

Step 3 - Substitute the value and calculate the surface area.

In this problem: Substitute \(r = 3.5\): \(SA = 4\pi \times 3.5^{2} \approx 153.94\).

\(SA = 4\pi \times 3.5^{2} \approx 153.94\)

Final answer:

\(SA \approx 153.94\)