Advanced SAT Math volume question

Question

Water is poured into a rectangular container 10 centimeters   long, 12 cm wide, and 9 cm high, until it is 1/20 full. All this water is then poured into an empty cylindrical container with a circular base of radius 3 cm. The height of the water in the cylindrical container is y/π centimeters, where y is a constant. What is the value of y?

Answer 1

[Having a word problem on a timed test like SAT, it is especially important to get fast to the Math core of what the question is about. And it better be on the first reading. In this case, get the following:]

We are asked about the Height of a cylinder with known Base and unknown Volume, which we can get from the Volume of a prism first.

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For water in the cylindrical container V_wc

Given: r = 3 cm, h = y/π cm

Volume of water in the cylindrical container is V_wc = πr²h = 9π _* y/π = 9y => y = V_wc / 9

Now, we need to find V_wc

Given: Volume of water in the cylindrical container V_wc is same as

Volume of water in the rectangular container V_wr => V_wc = V_wr

For water in the rectangular container V_wr

Given: l = 10 cm, w = 12 cm, h = 9 cm

Given: It is 1/20 full

Then V_wr = 1/20 _* V_r (volume of the rectangular container, a rectangular prism)

Volume of rectangular prism is V_r = l _* w _* h

Then

y = V_wc / 9 = V_wr / 9 = (1/20 _* V_r) / 9 = (1/20) _* (l _* w _* h) / 9

10 _* 12 _* 9 12

y = ------------------ = ---- = 6

20 _* 9 2

Answer: y = 6 cm

Answer 2

See the videa.

I worked it. On SAT day you can work similar questions.

Answer 3

First let's get the volume of water in the rectangular container. The total volume is

10 * 12 * 9 = 1080 cm³

The container is 1/20 full, so 1080/20 = 54 cm³.

The volume of a cylinder is V = πr²h,

We know that V = 54 and r = 3, so we can write this as

54 = 9πh

And solving for h gives 6/π, therefore y = 6.