Question

2. Pequot Lakes, Minnesota has a spherical water tower that is known as “the world’s largest fishing bobber.” The water tower holds 6,684 cubic feet of water. The water tower needs to be repainted, and it will have to be painted twice to get two coats of coverage. One gallon of paint can cover 350 square feet. How many gallons of paint will be needed to paint the water tower?

Answer 1

28.93 gallons of paint

Explanation:

The volume of a sphere can be found using the formula:

V = (4/3)πr^3

We are given that the water tower holds 6,684 cubic feet of water, so we can use this to find the radius:

6684 = (4/3)πr^3

(6684 * 3) / (4 * π) = r^3

r = (6684 * 3 / (4 * π))^(1/3) = 35.73 feet

Next, we need to find the surface area of the sphere. The surface area of a sphere can be found using the formula:

A = 4πr^2

So, the surface area of this water tower can be found as:

A = 4π * 35.73^2 = 4π * 1286.13 = 5071.57 square feet

Finally, we need to find the amount of paint needed to paint the surface area twice. One gallon of paint can cover 350 square feet, so we can divide the surface area by 350 to find the number of gallons of paint needed:

Gallons of paint = (5071.57 * 2) / 350 = (10143.14 / 350) = 28.93 gallons

So, 28.93 gallons of paint are needed to paint the water tower twice.