Problem Solving

BTGModeratorVI wrote: ↑

Thu Nov 26, 2020 1:16 pm

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

Answer: 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