1. Riley noticed an aquarium in his father’s office. The aquarium had the dimensions 16 in. by 8.5 in. by 10.5 in. The formula for volume is: V = l × w × h.
(a) Riley noticed that the aquarium was three-fourths full of water. How many more cubic inches of water would be required to fill the tank? Show your work.
(b) Another aquarium in the building has dimensions that are each triple the size of the aquarium in Riley’s father’s office. Riley thought that the volume would also triple. Is Riley correct? How many times greater is the volume of the larger aquarium than the smaller?

Question

1. Riley noticed an aquarium in his father’s office. The aquarium had the dimensions 16 in. by 8.5 in. by 10.5 in. The formula for volume is: V = l × w × h.     
(a)  Riley noticed that the aquarium was three-fourths full of water. How many more cubic inches of water would be required to fill the tank? Show your work.
(b) Another aquarium in the building has dimensions that are each triple the size of the aquarium in Riley’s father’s office. Riley thought that the volume would also triple. Is Riley correct? How many times greater is the volume of the larger aquarium than the smaller?

danjs · Answer

First off, find the volume of the tank [in^3] by multiplying together the 3 given numbers

danjs · Answer

Volume = length x width x height

length = 16
width = 8.5
height = 10.5

anonymous · Answer

1428

danjs · Answer

now find 3/4ths of that, multiply it by 0.75

anonymous · Answer

1428/4=357

danjs · Answer

close...

$$1428 *\frac{ 3 }{ 4 } = \frac{ 1428 * 3 }{ 4 }$$

anonymous · Answer

1071

danjs · Answer

Right, then 3/4ths of the tank is 1071 in^3 of water. How much is missing?

danjs · Answer

Full volume 1428 - 3/4ths volume 1071 = 357 in^3 left to fill the tank

danjs · Answer

Or you could have said, 1/4th of the water is missing, and did what you did above, and said 1/4th of 1428  is 357 in^3 of water

danjs · Answer

Do you know how to begin the second part?

anonymous · Answer

16*3

danjs · Answer

right, multiply all 3 of those dimensions by 3

danjs · Answer

Larger Tank

Length = 16*3  = 48   in
Width = 8.5*3  = 25.5   in
height = 10.5*3  = 31.5   in

anonymous · Answer

38,556

danjs · Answer

How many smaller tanks will fit in the larger tank?

anonymous · Answer

38,556-4284=34272

danjs · Answer

you don't want to subtract the two values, you want to see how many times 4284 will go into 38556, divide the larger by the smaller

anonymous · Answer

ooo

anonymous · Answer

9

danjs · Answer

or you could keep subtracting , and count how many times it takes subtracting to get to zero

danjs · Answer

Here is a summary of what you did...

danjs · Answer

wait

anonymous · Answer

ok

danjs · Answer

The smaller volume

v = 16 * 8.5 * 10.5  = 1428

The Larger Volume

V = 48 * 25.5 * 31.5 = 38556

The Larger Volume divided by the smaller volume

38556 / 1428  = 27

The larger tank is 27 times the volume of the smaller tank

danjs · Answer

What you basically did is...

Small volume :  
v = l x w x h

Large Volume
V = 3l x 3w x 3h = (3x3x3)*(l x w x h)  =  27

danjs · Answer

If you multiply the side lengths by 3, then the volume will be 3^3 or 27 times larger

danjs · Answer

In general

If you multiply the lengths by a factor of 'n'
the Larger volume will be n^3 times larger than the smaller volume

anonymous · Answer

ok

danjs · Answer

one of the numbers was wrong, you used the value from the first part, the 1/4th of the tank 1071 in the second part, we needed to use the whole volume 1428

danjs · Answer

sorry it is late, sleepy and missed it

danjs · Answer

feel free to mssg me and fan or whatever, i am usually on once a day at at least... ttyl

anonymous · Answer

ok thanks for the help

danjs · Answer

welcome