Geometry

[swerve]

Two oil cans, X and Y, are right circular cylinders, and the height and the radius of Y are each twice those of X. If the oil in can X, which is filled to capacity, sells for $2, then at the same rate, how much does the oil in can Y sell for if Y is filled to only half its capacity?

A. $1
B. $2
C. $3
D. $4
E. $8

The OA is E

Source: Official Guide

[Brent@GMATPrepNow]

Two oil cans, X and Y, are right circular cylinders, and the height and the radius of Y are each twice those of X. If the oil in can X, which is filled to capacity, sells for $2, then at the same rate, how much does the oil in can Y sell for if Y is filled to only half its capacity?

A. $1
B. $2
C. $3
D. $4
E. $8

The OA is E

Source: Official Guide

Volume of cylinder equals = π(radius²)(height)

Let Can X have radius 1 and height 1.
Volume of Can X = π(1²)(1) = π

This means Can Y has radius 2 and height 2.
Volume of Can X = π(2²)(2) = 8π

8π/π = 8, which means the volume of Can Y is 8 times the volume of Can X
Since Can Y is only HALF FULL, then Can Y contains 4 TIMES the volume that Can X contains

So, if Can X sells for $2, Can Y must sell for $8 (since $2 TIMES 4 is $8)

Answer: E

Cheers,
Brent

[Scott@TargetTestPrep]

Two oil cans, X and Y, are right circular cylinders, and the height and the radius of Y are each twice those of X. If the oil in can X, which is filled to capacity, sells for $2, then at the same rate, how much does the oil in can Y sell for if Y is filled to only half its capacity?

A. $1
B. $2
C. $3
D. $4
E. $8

The OA is E

Source: Official Guide

Solution:

We can let the radius of X = r and the height of X = h; thus, the radius of Y = 2r and the height of Y = 2h.

Thus, the volume of cylinder X is πr^2h and the volume of cylinder Y is:

π[(2r)^2](2h) = 8πr^2h

Since cylinder X is filled to its capacity, the volume of oil in X is πr^2h. However, since cylinder Y is only filled to half of its capacity, the volume of oil in Y is 4πr^2h. Since the oil in X sells for $2, at the same rate, the oil in Y should sell for 4 times as much (since it has 4 times as much oil), or $8.

Answer: E