Question

One gallon of paint covers 400 square feet of surface area. A typical spherical water tower holds 66,840.28 cubic feet of water. If a city has 25 gallons of paint available, will there be enough to paint the outside of a typical spherical water tower?

Answer 1

Answer:

27 feet

Step-by-step explanation:

Answer 2

Answer:

There will be enough paint to paint the exterior of a typical spherical water tower

Step-by-step explanation:

Step 1

Find the radius of the sphere

we know that

The volume of the sphere is equal to

$V=\frac{4}{3}\pi r^{3}$

In this problem we have

$V=66,840.28\ ft^{3}$

substitute in the formula and solve for r

$66,840.28=\frac{4}{3}\pi r^{3}$

$(\frac{3}{4 \pi})66,840.28=r^{3}\\ \\r=\sqrt[3]{(\frac{3}{4 \pi})66,840.28} \\ \\r=25.18\ ft$

Step 2

Find the surface area of the sphere

The surface area of the sphere is equal to

$SA=4\pi r^{2}$

we have

$r=25.18\ ft$

substitute

$SA=4\pi (25.18^{2})=7,967.49\ ft^{2}$

Step 3

Find the number of gallons of paints needed to paint the outside of a typical spherical water tower

by proportion

$\frac{1}{400}\frac{gallon}{ft^{2}}=\frac{x}{7,967.49}\frac{gallons}{ft^{2}}\\ \\x=7,967.49/400\\\\x=19.92\ gallons$

$19.92 < 25$

therefore

There will be enough paint to paint the exterior of a typical spherical water tower.