I need math help...?

Question

I have a short no more than five minute word problem. It is very easy..but i just need someone to check it...

Situation: Triangle tom lives in a triangualr house with some rectangular rooms. This living room is 10ft wide and 15 ft long. His game room is 20 ft by 30 ft- thus the dimensions are doubled.


Problem: Triangle toms living room is 20 ft high and his game room is double that: 40ft high. He wants to fill his game room half way up with colored plastic balls. Since all the dimensions are doubled he's only filling half the game room, he thinks the amount of space would be the same as that of the entire living room. Is he correct?

My answers: I said no, his prediction was wrong. The game room is 24,000 ft while his living room is 6000.

Answer 1

If all the dimensions are double, then the volume of the living room will be 1/8 that of the game room. (Your calc for vol of living room is wron. It will be 10x15x20 = 3000)

So, if he fills up the game room half way up, he will fill in 4 times the vol of the living room.

Answer 2

Part of your answer is right. His prediction is wrong, but your reason has a mistake. The volume of the living room is 3000 cubic feet, not 6000. Tom is incorrect because doubling each measure does not double the volume. If the length, width, and height are all multiplied by two, that's 2*2*2, or 8 altogether. The volume of the game room is 8 times as large as the living room volume. He would need to fill up his living room 4 times to get the number of balls that would equal half of his game room.

Answer 3

You answer is right but part of solution process was incorrect.

Game Room: 20*30*40=24000 Cu Ft (correct)
Living Room: 10*15*20= 3000 only

Answer 4

Need to go to cubic feet.

LR 10 ft wide by 15 ft long by 20 ft high = 10 X 15 X 20 cubic feet, or 3000 total.

GR 20 ft wide by 30 ft long by 40 ft high = 20 X 30 X 40 cubic feet, or 24000 cubic feet.

Your answer was right, but you missed the math on the LR.

Answer 5

You're wrong there. First off his living room is 3000 cubic ft.
But you're still right that his prediction is wrong.
If you double all the length dimensions for a brick shape, you'll in fact increase the volume 8 times (2*2*2, once for every dimension)

Answer 6

volume=width x length x height

volume he wants to fill is 20ft x 30ft x20ft = 12,000 cubic feet.

volume of living room is 10 x 15 x 20 = 3,000 cubic feet

No is the correct answer but where did the 6,000 cubic feet come from?

Answer 7

if only one dimension is doubled, then Tom is right.... by doubling EACH dimension, you increase the factor by two EACH dimension after .... by doubling the height, width and depth, you increase by a factor of 8 (2*2*2)...

the volume is 8 times larger, not doubled

Answer 8

NOT SQUARE FEET.., CUBIC FEET .., CU.FT.
NOW .., if you wish to make that interesting,
the spheres are solid.., 4 inch diameter..,
What percent of the spaces is actually filled..,
Just ruminate and ponder.. : )

Answer 9

LOL Sounds like you're going to have fun with that...I actually can't help you...It's a brain twister. I'd say that no was correct tho. Good luck! lol

Answer 10

I believe ur right . Living room = 6000ft
Game room = 12000ft

I hope that is right