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

Answer:

Number of marbles are 200000

Step-by-step explanation:

Rectangular box:

length = 5 feet

width =4 feet

height =3 feet

now, we can find volume of box

$V=L\times W\times H$

$V=5\times 4\times 3$

$V=60ft^3$

Volume of marbles:

We know that shape of marbles will be in sphere

we are given

diameter =1 inch

radius =0.5 inch

$r=\frac{0.5}{12} ft$

now, we can find volume

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

we can plug value

$V=\frac{4}{3}\pi (\frac{0.5}{12})^3$

$V=0.00030$

now, we can find number of marbles

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

So, number of marbles are

$=\frac{60}{0.00030}$

$=200000$