Alaine has 1 gallon of paint. She is going to pour it into a paint tray that measures 10 inches wide, 12 inches long, and 5 cm deep.

(1 gallon = 231 in3, 1 inch = 2.54 cm)

Which of the following scenarios will happen?

The paint will not fill the tray by 369 cm3.

The paint will not fill the tray by 5.22 in3.

The paint will fill the tray exactly.

The paint will overfill the tray by 5.22 in3.

Question

Alaine has 1 gallon of paint. She is going to pour it into a paint tray that measures 10 inches wide, 12 inches long, and 5 cm deep.

(1 gallon = 231 in3, 1 inch = 2.54 cm)

Which of the following scenarios will happen?

 The paint will not fill the tray by 369 cm3.

 The paint will not fill the tray by 5.22 in3.

 The paint will fill the tray exactly.

 The paint will overfill the tray by 5.22 in3.

jdoe0001 · Answer

how many inches in 5cm?

anonymous · Answer

1.9

jdoe0001 · Answer

so 1.9 inches

so our tray in inches can hold up to   10 x 12 x 1.9   = $\bf 228 in^3$ of paint

so, now let's find out, how many cm in 10 inches, and 12 inches?

anonymous · Answer

in 10 there is 25 cm and in 12 there is 30

jdoe0001 · Answer

ok, then our tray in in cm will hold up to 25 x 30 x 5  = $\bf 3750 cm^3$ of paint

so,  Alice is about to dump in the tray 1gallon, that is 
$\bf 231 in^3 \ or \ 587cm^3$

will it fit, overflow or not fit?

jdoe0001 · Answer

hmmm, lemme correct something really quick

anonymous · Answer

ok

jdoe0001 · Answer

your numbers are rounded up, so lemme not round them up and use the decimal values
since I think they're expected

anonymous · Answer

okay so will it overflow

jdoe0001 · Answer

$\bf 10 \times 12 \times 1.968 = 236.22 in^3\
25.4 \times 30.48 \times 5 = 3870.96 cm^3$

Alice is about to pour $\bf 231 in^3 \ or \ 586.74 cm^3$

anonymous · Answer

586.74cm?

jdoe0001 · Answer

ohhh smokes.... you're right.. the figure man!   yes one sec

anonymous · Answer

Which of the following scenarios will happen?

 The paint will not fill the tray by 369 cm3.

 The paint will not fill the tray by 5.22 in3.

 The paint will fill the tray exactly.

 The paint will overfill the tray by 5.22 in3.

jdoe0001 · Answer

$\bf 231 \times 2.54^3  = 3785.41\\quad \
10 \times 12 \times 1.968 = 236.22 in^3\
25.4 \times 30.48 \times 5 = 3870.96 cm^3$

she's about to pour $\bf 231 in^3 \ or \ 3785.41 cm^3$

anonymous · Answer

so which would it be

jdoe0001 · Answer

well, obviously the tray can take more than 231 cubic inches, so it will fit

notice that, the tray can hold 236.22
the paint is just 231

the difference is 5.22

the tray holds the paint, and still have more room for 5.22 cubic inches

so $\bf \text{The paint will not fill the tray by 5.22 in3.}$

anonymous · Answer

okay thank you!

jdoe0001 · Answer

yw