Question

Your grandfather has been collecting marbles all his life. He owns an old chest that measures 5 feet by 4 feet by 3 feet high. Each of the marbles I collected, measures 1 inch in diameter. I have finally filled the chest to the top. A pproximately how many marbles are in the chest?

Answer 1

Number of marbles are 200000

Explanation:

Rectangular box:

length = 5 feet

width =4 feet

height =3 feet

now, we can find volume of box

`V=L* W* H`

`V=5* 4* 3`

`V=60ft^3`

Volume of marbles:

We know that shape of marbles will be in sphere

we are given

diameter =1 inch

radius =0.5 inch

`r=(0.5)/(12) ft`

now, we can find volume

`V=(4)/(3)\pi r^3`

we can plug value

`V=(4)/(3)\pi ((0.5)/(12))^3`

`V=0.00030`

now, we can find number of marbles

Number of marbles = ( volume of box)/( volume of marbles)

So, number of marbles are

`=(60)/(0.00030)`

`=200000`