Question

ASAP I NEED TO GRADUATE THIS WEEK

1. How many dice 2 cm long, 2 cm wide, and 2 cm high would
fit into a box 20 cm long, 12 cm wide, and 8 cm high?
a. 240
b. 320
c. 400​

Answer 1

Part 1) Option a.
`240\ dices`

Part 2) Option c.
`9.156.24\ pounds`

Explanation:

Part 1)

step 1

Find the volume of one dice

The volume is equal to

`V=b^(3)`

we have

`b=2\ cm`

substitute

`V=2^(3)=8\ cm^(3)`

step 2

Find the volume of the box

The volume is equal to

`V=LWH`

we have

`L=20\ cm`

`W=12\ cm`

`H=8\ cm`

substitute

`V=20*12*8=1,920\ cm^(3)`

step 3

Find the number of dices

Divide the volume of the box by the volume of one dice

`1,920/8=240\ dices`

Part 2)

step 1

Find the volume of the cylinder

The volume is equal to

`V=\pi r^(2) h`

we have

`r=9\ ft`

`h=12\ ft`

assume

`\pi =3.14`

substitute

`V=(3.14)(9)^(2)(12)`

`V=3,052.08\ ft^(3)`

step 2

Find how many pounds of sand will fit into the cylinder

using proportion

`(3)/(1)(pounds)/(ft^(3))=(x)/(3,052.08)(pounds)/(ft^(3))\\ \\x=3,052.08*3\\ \\x=9.156.24\ pounds`