Question

You cut a circular hole 1/4 -inch in diameter in a piece of cardboard. With the cardboard 30 inches from your face, the Moon fits exactly into the hole. The Moon is about 240,000 miles from Earth. Is the Moon's diameter more than 1,500 miles?

Answer 1

The Moon's diameter is greater than
`1,500` miles

Explanation:

we know that

`1\ mile=63,360\ inches`

`1,500\ miles=1,500*63,360=95,040,000\ inches`

`240,000\ miles=240,000*63,360=15,206,400,000\ inches`

by proportion

Find the Moon's diameter

Let

x-----> the Moon's diameter in inches

`(x)/(15,206,400,000)=(0.25)/(30)\\ \\x= 15,206,400,000*0.25/30\\ \\x=126,720,000\ inches`

Compare

`126,720,000\ inches> 95,040,000\ inches`

therefore

The Moon's diameter is greater than
`1,500` miles