If the radius of a cylinder is half the length of the edge

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

If the radius of a cylinder is half the length of the edge

by Gmat_mission » Sat Apr 06, 2019 5:00 am

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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

[spoiler]OA=C[/spoiler]

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Sat Apr 06, 2019 5:00 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Wed Apr 10, 2019 7:51 am

$$Radius\ of\ cylinder\ =\ \frac{1}{2}\cdot length\ of\ edge\ of\ a\ cube$$
$$Height\ of\ cylinder\ =length\ of\ edge\ of\ a\ cube$$
$$Ratio\ of\ volume\ of\ cube\ and\ cylinder=??$$
$$Volume\ of\ cube=\left(length\ of\ cube\right)^3=a^3$$
$$Volume\ of\ cylinder=\pi r^2h$$
$$r=a\cdot\frac{1}{2}=\frac{a}{2}\ and\ h=a$$
$$Volume\ of\ cylinder=\pi\cdot\left(\frac{a}{2}\right)^2\cdot a$$
$$Volume\ of\ cylinder=\pi\cdot\frac{a^3}{4}\ where\ a^3=volume\ of\ cube$$
$$=\frac{\pi}{4}\cdot volume\ of\ cube$$
$$The\ ratio\ of\ volume\ of\ cube\ to\ volume\ of\ cylinder=\frac{4}{\pi}$$

Hence, the correct answer is C

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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 » Sat Apr 13, 2019 5:38 pm

Gmat_mission 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

[spoiler]OA=C[/spoiler]

Source: Princeton Review

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 the cylinder is:

x^3/(x^3 * Ï€/4)

1/(Ï€/4)

4/Ï€

Answer: C

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