Question

The cube has a surface area of 24 cm2.

What would the surface area of the prism be if each dimension were quadrupled?

Answer 1

http://static.k12.com/calms_media/media/1575000_1575500/1575041/1/1fc43cdf04f756b0f3bac779ba66aa59a1d955df/MS_IMB-1400106-1120705.jpg

Answer 2

576?

Answer 3

Hi Welcome to Openstudy!

\(\sf Surface\ Area= 6a^2\)

If we quadruple the dimension it will be like:
\(\sf Surface\ Area"= 6(4a)^2\\Surface\ Area"= 6(16a^2)\\Suraface\ area"= 96a^2\)

"a" is the dimension which is 2 cm

I got a different answer. Can you show me how did you get 576?

Answer 4

whats your answer

Answer 5

i did 24*24

Answer 6

a= 2 cm

\(\sf Surface\ Area= 6a^2\) -> if you plug 2 cm here you'll get 24cm^2

If we quadruple the dimension it will be like:
\(\sf Surface\ Area"= 6(4a)^2\) <- if you evaluate this, you'll get the right answer.

Answer 7

2^4 = ? @i-love-skittles-lol-1

Answer 8

what is 2^4 ? its 16

Answer 9

, and the formula for the surface area of a cube is:

SA = 6a^2

Where 'a' is the side length, plug it in.

Answer 10

6(16)2 are you getting it?

Answer 11

@Hannah_Waller May I ask why would you do 2^4 ?

The question says "each dimension were quadrupled"
so if we solve the surface area without the formula
it goes like this:

Dimension will be: 2 x 4 = 8
so each dimension is 8

A cube has 6 equal sides and each side of a cube is a square. Formula for the area of square is \(\sf a^2\)

so the S.A. would be: \(\sf a^2 + a^2+ a^2+ a^2+a^2+a^2\) where the value of a this time is 8 cm not 16 cm.