Are you smarter than 8th grader? (Math Question)?

Question

An aquarium has a rectangular base that measures 100 cm by 40 cm and hans a height of 50 cm. The aquarium is filled with water to a death of 37cm. A rock with volume 1000 cm3 is then placed in the aquarium and completely submerged. By how many centimeters does the water lever rise?

Answer 1

Cute question title! :)

The volume of the water initially is
V=l * w * h
V = 100*40*37 (although the TANK is 50 cm high, the water height is only 37cm)
V = 148,000 cm cubed

When you add in the volume of the rock, it's another 1000 cm, so add it to the volume of the water, and now the total volume in the tank is 149,000

Use the formula going backwards to find the new height:

V = l*w*h
149,000 = 100 * 40 * h
so h = 149,000/ (4000)
h = 37.25 cm cubed.

The new height is 37.25, and the original height was 37, so the difference is 0.25 cm

Of course, there's another way to do this too...

if the rock is 1000 cm cubed, then just figure out what height that extra 1000 cm cubed of volume would be on its own in the tank:

1000 = 100*40*h
h = 1000/4000
h = 0.25

Then, so the water rises by 0.25 cm.

Answer 2

Volume of water = length x width x height
= 100 x 40 x 37
=148 000 cm^3

Volume of water in depth of 1 cm = 100 x 40 x 1
=4000 cm^3 (so it takes 4000 cm^3 to raise water level 1 cm)
Since 4000 cm^3 needed to raise level by one cm, and only 1000 cm ^3 are added, the level doesn't even rise 1 cm. It rises 1/4 of a centimeter.

I think that's right.

Answer 3

Volume = Base x Height
=> Height = Volume / Base = 1000 cm³ / (100 cm x 40 cm)
= 0.25 cm ---> Answer

(100 cm x 40 cm x 50 cm = 3.2 ft x 1.3 ft x 1.6 ft, not a small tank!)

XR

Answer 4

No, apparently I'm not smarter than an 8th grader...sorry.