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: blank square feet

Explanation:

Step1: Find the radius

The radius $r$ of a sphere is half of the diameter. Given $d = 30$ feet, so $r=\frac{d}{2}=\frac{30}{2}=15$ feet.

Step2: Use the surface - area formula for a sphere

The surface - area formula of a sphere is $A = 4\pi r^{2}$. Substitute $r = 15$ into the formula: $A=4\pi(15)^{2}=4\pi\times225 = 900\pi$.

Step3: Calculate the numerical value

Using $\pi\approx3.14159$, we have $A\approx900\times3.14159 = 2827.431$. Rounding to the nearest square foot, $A\approx2827$.

Answer:

2827