Cubical Block

[nycmathguy]

A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

Let me see. Everything I am about to do is my guess. This problem is not clear to me.

A cube has 6 sides.

6 /w = 6/12

6w = 6(12)

6w = 72

w = 72/6

w = 12 pounds

You say?

 

[MathLover1]

If the original cube weighs 6 pounds and you double the sides of the cube, then you double in three directions, so you now have 8 of the original cubes.
Hence the weight of the new cube is 8*6=48 pounds.

or this way, compare the volumes
if side is a
V=a^3
if side a doubles, we have 2a
then V=(2a)^3=8a^3

the weight of the new cube is 8 times more

8*6=48 pounds

 

[nycmathguy]

If the original cube weighs 6 pounds and you double the sides of the cube, then you double in three directions, so you now have 8 of the original cubes.
Hence the weight of the new cube is 8*6=48 pounds.

or this way, compare the volumes
if side is a
V=a^3
if side a doubles, we have 2a
then V=(2a)^3=8a^3

the weight of the new cube is 8 times more

8*6=48 pounds
View attachment 358

Ok. I tried. You will see exactly how weak I am at solving applications. This is my main struggle---word problems.

 

[HallsofIvy]

You seem to have assume that this was a hollow block so that only the sides have weight, not the interior.

 

[nycmathguy]

You seem to have assume that this was a hollow block so that only the sides have weight, not the interior.

Brother, I never assume. I always do my best. If I start to assume, then I will make an ass of u and me. Get it?