Question

PLEASE HELP: Brooks built two similar wooden chests in the shape of rectangular prisms. She used 5 pints of paint to cover the outside of the larger chest fully and 2 pints to cover the outside of the smaller chest. How much more volume does the larger chest contain?

A. 158% more
B. 250% more
C. 300% more
D. 395% more

Answer 1

depends, does the chest have a top?

Answer 2

another one that is sort of guessing but pretty certain just do 5/2=2.5 then times 100 for 150%

Answer 3

250% *

Answer 4

It's not 250%

Answer 5

2 similar chests

meaning the sides of the smaller chest is smaller by a specific ratio which i will denote as "a"

Answer 6

okay

Answer 7

now, denoting the sides of the chest
L x W x H as length width and height

now assuming that the chest has a top

the surface area of the rectangular prism or chest is
SA = 2LW +2LH + 2 WH

Answer 8

we know the surface area of the larger chest takes 5 pints

and the surface area of the smaller chest takes only 2 pints to cover

Answer 9

is it?

Answer 10

300%

Answer 11

That's what i got.

Answer 12

i have no idea, i didnt actually solve it yet

Answer 13

Haha.

Answer 14

im kinda solving it as i go

Answer 15

anyways

SA of the smaller chest would be
SAsmaller = a^2(2LW +2LH + 2 WH)

Answer 16

now just assuming that SAlarger = 5
and SAsmaller = 2

substuting them in we get

2=a^2(2LW +2LH + 2 WH)
5=(2LW +2LH + 2 WH)

Answer 17

now we solve for a

Answer 18

ok

Answer 19

2/5 = a^2

Answer 20

it wasnt 250 tho. I tried that and got it incorrect.

Answer 21

i know, its definitely not 250%

Answer 22

anyways since we know a = sqrt{2/5}

Answer 23

recall that the volume of a rectangular prism is V= L*W*H

Answer 24

k

Answer 25

so the smaller volume would be

Vsmall=aL * aW *a H = a^3 LWH

and the larger volume would just be
Vlarge= L*W*H

Answer 26

now to find the percentage of increase of area

you would need to divide the volume of the large by the volume of the small

Vlarge/ V small

Answer 27

= 1/ a^3

Answer 28

k

Answer 29

So it was 158%

Answer 30

It's either A or C. I think its A.

Answer 31

tell me, a= ?

Answer 32

percentage is 158

Answer 33

i got something different

Answer 34

rlly? :/

Answer 35

a = sqrt{2/5}

Answer 36

a= .63245 ...

so the solution would be 1/a^3

Answer 37

Haha.. okay... so if it isnt A/B/D. Then it must be 300% 282 ?

Answer 38

why is it not A B D ?

Answer 39

i got something diffrnt

Answer 40

Because B i already got wrong. You said 158% was incorrect. and i dont think its 395% because its too high. So what's left is 300%

Answer 41

dont assume

Answer 42

what do you mean?

Answer 43

a^3 = .25297557 ...

Answer 44

so it was 395

Answer 45

grab a calculator

1/ .25297557 = ?

Answer 46

which is why you dont assume

Answer 47

just read through the steps again

Answer 48

i wasnt assuming. i just didnt round to get the answer. thats why i kept getting 250 as my answer. thanks :)