Questions: Find the surface area of the sphere with diameter 22 meters. Leave your answer in terms of π. 176 π m² 1331 π m² 1936 π m² 484 π m²

Transcript text: Find the surface area of the sphere with diameter 22 meters. Leave your answer in terms of $\pi$. $176 \pi m^{2}$ $1331 \pi m^{2}$ $1936 \pi m^{2}$ $484 \pi m^{2}$

Solution

Solution Steps

To find the surface area of a sphere, we use the formula $4 \pi r^2$, where $r$ is the radius of the sphere. Given the diameter, we can find the radius by dividing the diameter by 2. Then, we substitute the radius into the formula to find the surface area.

Step 1: Calculate the Radius

Given the diameter of the sphere is 22 meters, we calculate the radius $ r $ by dividing the diameter by 2: \[ r = \frac{22}{2} = 11 \, \text{meters} \]

Step 2: Use the Surface Area Formula

The formula for the surface area $ A $ of a sphere is: \[ A = 4 \pi r^2 \] Substituting the radius $ r = 11 $ meters into the formula: \[ A = 4 \pi (11)^2 \]

Step 3: Simplify the Expression

Simplify the expression to find the surface area in terms of $ \pi $: \[ A = 4 \pi \times 121 \] \[ A = 484 \pi \, \text{m}^2 \]