Question

A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. Which of these best describes the volume of this rectangular prism?

1 unit cube and 15 smaller cubes of volume fraction 1/125 cubic inch each

1 unit cube and 75 smaller cubes of volume fraction 1/125 cubic inch each

7 unit cubes and 25 smaller cubes of volume fraction 1/125 cubic inch each

7 unit cubes and 125 smaller cubes of volume fraction 1/125 cubic inch each

Answer 1

do you know the formula for the volume of a cube ?

Answer 2

nope, Thats all the question brings

Answer 3

yes, I see that. But you are supposed to bring the formula for the volume of a cube
in other words, they expect you to know that.
can you look it up ?

Answer 4

Volume of a cube = side times side times side. Since each side of a square is the same, it can simply be the length of one side cubed. If a square has one side of 4 inches, the volume would be 4 inches times 4 inches times 4 inches, or 64 cubic inches.

Answer 5

ok, using that , what is the volume of one of the tiny cubes they mention ?

Answer 6

16

Answer 7

cubes of edge length fraction 1/5 inch

they are saying each side is 1/5 inch long.

Answer 8

Volume of a cube = side times side times side

Answer 9

oh ok

Answer 10

any idea what the volume of that cube is ?

Answer 11

is it 0.8 inches

Answer 12

what is the length of one side ?

Answer 13

1/5 inch long

Answer 14

and what is side * side * side
when side is 1/5 ?

Answer 15

so i multiply 1/5 x 3 or 4

Answer 16

you are doing
\[ \frac{1}{5} \cdot \frac{1}{5}\cdot \frac{1}{5} \]

first do
\[ \frac{1}{5} \cdot \frac{1}{5} \]

Answer 17

when multiplying fractions, multiply top times top and bottom times bottom

Answer 18

i multiplied 1/5 x 1/5 and I got 0.04

Answer 19

I would keep it as a fraction, because the answer choices are fractions
what is the answer as a fraction?
(people learn how to do this in their head)

the top is 1*1
the bottom is 5*5

Answer 20

1/25

Answer 21

1/125

Answer 22

yes 1/5*1/5 is 1/25
and 1/25* 1/5 is 1/125

that is the volume of one cube

any idea how to find the volume of 200 of these cubes ?

(I would multiply 200*1/125)

Answer 23

1.6

Answer 24

ok, but it's still hard to pick out the correct choice

I think they want you to do
\[ 200 \cdot \frac{1}{125}= \frac{200}{125} \]
125 divides into 200 1 with a remainder. any idea what the remainder is ?

Answer 25

i dont get the 200 1 part

Answer 26

in other words, 125 goes into 200 once
but there is some amount left over

Answer 27

Have you ever seen