1971 AMC 12 Problem 15

Question

An aquarium on a level table has rectangular faces and is

10

inches wide and

8

inches high. When it was tilted, the water in it just covered an

8

-inch by

10

-inch end but only three-fourths of the rectangular bottom. The depth of the water when the bottom was again made level was:

2\tfrac12

inches

3

inches

3\tfrac14

inches

3\tfrac12

inches

4

inches

Compare the water volume in the tilted and level positions

The tilted side view is a triangle with height

8

and base three-fourths of the aquarium length

Let the aquarium length be

L

and the level-water depth be

h.

In the tilted position the longitudinal cross-section of the water is a triangle with base

\frac{3L}{4}

and height

8.

Therefore

10\left(\frac12\cdot\frac{3L}{4}\cdot8\right)=10Lh,

so

h=3

inches.

Therefore, the correct answer is B.

Problem 15 in other years