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: Find the radius

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

Step2: Use the surface - area formula for a sphere

The surface - area formula for a sphere is $A = 4\pi r^{2}$. Substitute $r = 15$ into the formula: $A=4\pi(15)^{2}$.

Step3: Calculate the value

First, $(15)^{2}=225$. Then $4\pi(15)^{2}=4\pi\times225 = 900\pi$. Using $\pi\approx3.14159$, we get $A\approx900\times3.14159 = 2827.431$.

Step4: Round to the nearest square foot

Rounding $2827.431$ to the nearest square foot gives $2827$.

Answer:

2827