Which shows the dimensions of two rectangular prisms that have volumes of 320 mm3 but different surface areas?

A.
16 mm by 5 mm by 4 mm;
5 mm by 4 mm by 16 mm

B.
10 mm by 4 mm by 6 mm;
6 mm by 10 mm by 4 mm

C.
8 mm by 10 mm by 4 mm;
10 mm by 8 mm by 4 mm

D.
8 mm by 10 mm by 4 mm;
20 mm by 8 mm by 2 mm

Question

Which shows the dimensions of two rectangular prisms that have volumes of 320 mm3 but different surface areas?
 
 A.
16 mm by 5 mm by 4 mm; 
5 mm by 4 mm by 16 mm
 
 B.
10 mm by 4 mm by 6 mm; 
6 mm by 10 mm by 4 mm
 
 C.
8 mm by 10 mm by 4 mm; 
10 mm by 8 mm by 4 mm
 
 D.
8 mm by 10 mm by 4 mm; 
20 mm by 8 mm by 2 mm

anonymous · Answer

@e.mccormick @bagajr @kag plz help

anonymous · Answer

im not sure about this 1

anonymous · Answer

To find the volume of each one, just multiply the three numbers together. Do you think you can do that for all 8 of them?

anonymous · Answer

they all show 320 :'(

anonymous · Answer

Don't be confused; that's just the first half of the problem. Are you sure all of them are 320? Try calculating it again for the prisms in B.

anonymous · Answer

lol messed tht 1 up its 240

anonymous · Answer

Good, so you eliminated B.

anonymous · Answer

yep

anonymous · Answer

Now for the second half. The surface area of a rectangular prism (where the dimensions are x, y, and z) is:$$\Large2xy +2xz + 2yz$$

anonymous · Answer

:0 letters..i never understand those

anonymous · Answer

The first number is x, the second is y, and the third is z. What I wrote up there means (2 times x times y) plus (2 times x times z) plus (2 times y times z). For example, the surface area of the first one in A is$$\Large(2 \times x \times y) + (2 \times x \times z) + (2 \times y \times z)$$$$\Large (2 \times 16 \times 5)+(2 \times 16 \times 4)+(2 \times 5 \times 4)$$$$\Large160+128+40$$$$\Large328$$

anonymous · Answer

656?...whats tht about

anonymous · Answer

but  i still dont get it  how do i get the answer to this

anonymous · Answer

plz just can u explain this a little  easier

anonymous · Answer

Sorry, I had to leave for a couple minutes. Do you get what I did for A?

anonymous · Answer

^look above..

anonymous · Answer

Do you get how I got the surface area for the first one?

anonymous · Answer

no :'( im just stupid then im never gonna get this right

anonymous · Answer

Do you know how to get the area of each face of the prism?

anonymous · Answer

no thts why im asking for help ive been on this question for 45 min

anonymous · Answer

30*

wolf1728 · Answer

Look at the original problem.
Notice that in 3 of the 4 answers the numbers are the same except in choice D.

anonymous · Answer

wow...ty for tht

wolf1728 · Answer

Thanks :-)

anonymous · Answer

so are u saying its d?

anonymous · Answer

Sorry it keeps logging me out and disconnecting me for some reason. Thanks to wolf1728's observation, I guess calculations aren't actually necessary, lol. Yes, it would be D.

anonymous · Answer

ty both of u

anonymous · Answer

ok imma bout to post my answers i have to get an 80 to pass ill tell u what i get in a second

anonymous · Answer

i got A 100 WOOOOOOHOOOOOO

wolf1728 · Answer

By the way to save you some time, here's a calculator that gives volume and surface area at the same time - http://1728.org/recsolid.htm

anonymous · Answer

wow ty ill bookmark it

smartyprincess · Answer

me too!
 ty!