If the radius of a cylinder is half the . . . .

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

If the radius of a cylinder is half the . . . .

by VJesus12 » Sat Jan 06, 2018 3:45 am

If the radius of a cylinder is half the length of the edge of a cube, and the height of the cylinder is equal to the length of the edge of the cube, what is the ratio of the volume of the cube to the volume of the cylinder?

A. 2/Ï€

B. Ï€/4

C. 4/Ï€

D. Ï€/2

E. 4

The OA is the option C .

What are the formulas I should set here to get the ratio? Experts, can you show me how would you solve this PS question? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Sat Jan 06, 2018 3:45 am

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Jan 06, 2018 11:37 am

Hi VJesus12,

We're told that the radius of a cylinder is half the length of the edge of a cube and the height of the cylinder is equal to the length of the edge of the cube. We're asked for the ratio of the volume of the cube to the volume of the cylinder. This question requires a couple of formulas and can be solved by TESTing VALUES.

IF....
Side of the cube = 2
Radius of the cylinder = 1
Height of the cylinder = 2

Volume of the cube = (side)^3 = (2)^3 = 8
Volume of the cylinder = (pi)(R^2)(H) = (pi)(1^2)(2) = 2pi

Ratio of cube volume to cylinder volume = 8:2pi = 4:pi

Final Answer: C

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

Contact Rich at [email protected]

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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 » Sun Aug 11, 2019 6:33 pm

VJesus12 wrote:If the radius of a cylinder is half the length of the edge of a cube, and the height of the cylinder is equal to the length of the edge of the cube, what is the ratio of the volume of the cube to the volume of the cylinder?

A. 2/Ï€

B. Ï€/4

C. 4/Ï€

D. Ï€/2

E. 4

We can let x = the length of the edge of the cube. Thus, the volume of the cube is x^3. Furthermore, the radius of the cylinder is x/2, and the height of the cylinder is x. Since the volume of a cylinder is V = Ï€r^2h, the volume of the cylinder is:

V = Ï€(x/2)^2 * x

V = Ï€(x^2/4) * x

V = x^3 * Ï€/4

Thus, the ratio of the volume of the cube to that of the cylinder is:

x^3/(x^3 * Ï€/4)

1/(Ï€/4)

4/Ï€

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]