Question

Ruby red paint costs $0.50 per square inch. A ball is painted ruby red and costs $100.00 to paint. What is the diameter of the ball? Round to the nearest tenth of an inch.. A.4.0 in.. B.5.6 in.. C.8.0 in.. D.16.0 in.

Answer 1

Option C is the answer.

Explanation:

A ball is painted ruby red and costs $100.00 to paint and Ruby red paint costs $0.50 per square inch.

This means for an area of
`4\pi r^(2)`, $100 were used.
`4\pi r^(2)` because the ball is a sphere.

where r is the radius.

We know that , Area of ball * cost of paint per square inch = total cost of paint.

`4\pi r^(2) *0.5=100`

`2\pi r^(2)=100`

`r^(2)= (100)/(2\pi )`

`r^(2)=15.923` ;
`r=3.99` inch

Radius is 3.99 inches. or we can round this to 4 inches.

Hence, the diameter will be =
`2*4=8` inches.

Therefore, option C: 8 inches is the answer.

Answer 2

The diameter can be obtained by the formula A = pi*r^2

First, multiply 0.50 * 100 to obtain the area of the ball, then simplify and solve for the radius. Doubling the radius would yield the diameter. This is shown below:

Area of the ball = 0.50 * 100 = 50 in^2
A = pi*r^2
50 = (3.14)*r^2
r = 3.99 = approx. 4
diameter = 2r
Diameter = 8 inches.

Among the choices, the correct answer is C. 8.0 in.