Geometry

Hi roland2rule

We're told that a right circular cylinder is 3/4 FULL of soda, the volume of SODA in the can is 72Ï€ cubic inches and the diameter of the can is 8 inches. We're asked for the height, in inches, of the can.

Volume of a cylinder = (Ï€)(R^2)(H)

Here, we have a radius of 4 and a total volume of soda, so we can figure out the height of the SODA...

72Ï€ = (Ï€)(4^2)(H)
72Ï€ = (16Ï€)(H)
72Ï€/16Ï€ = (H)
Height of the SODA = 36/8 = 18/4 = 9/2 = 4.5 inches

Since the can is 3/4 full, we know that the height of the can has to be GREATER than 4.5 inches. There's only one answer that matches..

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorRO wrote:A soda can, in the shape of a right circular cylinder, is 3/4 full of soda. If the volume of soda in the can is 72Ï€ cubic inches and the diameter of the can is 8 inches, then what is the height, in inches, of the can?

A. 1.5
B. 3
C. 4
D. 4.5
E. 6

First, let V = the volume of the entire soda can. Since the volume of soda is 72Ï€ cubic inches and that represents 3/4 of the volume of the entire soda can, we see that:

(3/4)V = 72Ï€

3V = 288Ï€

V = 96Ï€

Now, using the volume formula of a cylinder, we can solve the height of the can:

V = π r^2 h

96π = π (4)^2 h

96Ï€ = 16Ï€ h

6 = h

Answer: E