Question

the shape of a water tower can partially be modeled by a sphere in which the diameter is 30 feet. a painter needs to calculate the surface area of this part of the water tower to accurately estimate the amount of paint needed for the job. what is the surface area of this portion of the water tower to the nearest square foot? surface area square feet

Explanation:

Step1: Recall sphere surface - area formula

The surface - area formula of a sphere is $A = 4\pi r^{2}$, where $r$ is the radius of the sphere.

Step2: Calculate the radius

Given the diameter $d = 30$ feet, the radius $r=\frac{d}{2}=\frac{30}{2}=15$ feet.

Step3: Substitute the radius into the formula

$A = 4\pi r^{2}=4\pi\times(15)^{2}=4\pi\times225 = 900\pi$ square feet.

Step4: Approximate the value

Using $\pi\approx3.14$, we have $A\approx900\times3.14 = 2826$ square feet.

Answer:

2826 square feet