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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Geometry

by BTGmoderatorRO » Sun Dec 24, 2017 9:45 am

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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

OA is E
DO I need the solid shapes formula to solve this? An Expert contribution will be highly appreciated.

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Source: Beat The GMAT — Problem Solving | Sun Dec 24, 2017 9:45 am

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by [email protected] » Sun Dec 24, 2017 4:07 pm

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

Contact Rich at [email protected]

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GMATWisdom: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Nov 29, 2017 4:38 pm; Thanked: 14 times

by GMATWisdom » Mon Dec 25, 2017 9:02 am

Roland2rule 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

OA is E
DO I need the solid shapes formula to solve this? An Expert contribution will be highly appreciated.

formula for right circular cylinder volume= Ï€r^2*h where r is rhe radius and h is the height.
thus (3/4)* Ï€r^2*h =72Ï€ given diameter=8 or radius r = 4 inch
(3/4)* Ï€4^2*h =72Ï€
(3/4)* Ï€16*h =72Ï€
or 12Ï€ h=72Ï€
or h=6
hence option E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jul 19, 2018 11:39 am

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 = Ï€ r^2 h

96Ï€ = Ï€ (4)^2 h

96Ï€ = 16Ï€ h

6 = h

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]