Question

@whpalmer4

Answer 1

Box A has a volume of 48 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were doubled. What is the volume of box B?


i got 96 m cubed?

Answer 2

yes he is a great helper

Answer 3

\[V_1=s^3\]
\[V_2 = (2s)^3 = 2^3*s^3 = 8s^3 = 8V_1\]

Does that seem like it is going to be only twice the volume? Think of making a box out of a kid's blocks. the smallest box is a 1 by 1 by 1, right? If you double each dimension, how many blocks do you need?

Answer 4

well, hard to draw the 2x2x2 version, but maybe you get the idea

Answer 5

doubling the side length of the cube makes the volume change by 2*2*2 = 8

Answer 6

I never have much luck explaining this, but when you scale the dimensions by a factor, you can find the new area or volume or whatever by just putting the scaling factors into the formula for the area, volume, etc.

For example, a rectangular prism has volume \[V=l*w*h\]if we double the length, and triple the height, and keep the width the same, we can find the new volume in terms of the old volume like this:
\[V = 2*1*3 = 6\]that's 6 times the old volume, not 6 as an absolute quantity

If we have a pizza with radius \(r\), the area is \(A = \pi r^2\) If we want to find the result of doubling the radius, we just us \(r = 2\), and our new area is \(A_{new} = r^2 = 2^2 = 4\) times the area of the old one. We get to ignore the constants because they are the same for both.

Answer 7

Does that make sense?

Answer 8

hold on i'm still reading it

Answer 9

ok i got 24 m cubed is that correct? @whpalmer4

Answer 10

no...

box A is 48 m^3

we double the length of each dimension of box A to create box B, correct?

Answer 11

so it is 96m cubed

Answer 12

you're not paying attention. what does the problem ask you to do? "to create box B, box A's dimensions were doubled"

Each dimension is doubled! Length, width, and height!

Think about it. If you have a box that is 1 unit on a side, and you need to make one that is 2 units on a side, how many of the original box would you have to stack up to make it?

Answer 13

Instead of having 1 box, you have a 2x2 layer of boxes on top of another 2x2 layer of boxes, right?

Answer 14

How many boxes is that in all?

Answer 15

288?

Answer 16

no, it's not 288 boxes! it's 8 boxes of 48 m^3 each

what is the total volume of 8 boxes of 48 m^3 each?

Answer 17

oh lol i had it all wrong ok ok well i got 384m cubed

Answer 18

What is the shape of the cross section taken perpendicular to the base of a cone?


i got triangle

Answer 19

yes, 384 m^3 is correct. 8 times the volume of the original, because 2^3 = 8

Answer 20

yes, that's the right cross section. Time for me to go, good night!

Answer 21

good night