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

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If the radius of a cylinder is half the length of the edge of a cube,  [#permalink]

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New post 15 Nov 2018, 04:15
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A
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C
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Question Stats:

68% (01:26) correct 32% (01:41) wrong based on 59 sessions

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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. \(\frac{2}{\pi}\)

B. \(\frac{\pi}{4}\)

C. \(\frac{4}{\pi}\)

D. \(\frac{\pi}{2}\)

E. 4

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Re: If the radius of a cylinder is half the length of the edge of a cube,  [#permalink]

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New post 15 Nov 2018, 04:26

Solution


Given:
    • Radius of the cylinder = \((\frac{1}{2})\) * length of the edge of a cube
    • Height of the cylinder = length of the edge of the cube

To find:
    • The ratio of volumes of cube and cylinder

Approach and Working:
    • Volume of cube = \(a^3\), where a is the side length
    • Volume of cylinder = \(ᴨ * r^2 * h\), where r is radius and h is the height

Given that, \(r = \frac{a}{2}\) and h = a

    • Implies, volume of cylinder = \(ᴨ * (\frac{a}{2})^2 * a = ᴨ * \frac{a^3}{4} = (\frac{ᴨ}{4})\) * volume of the cube

Therefore, ratio of volume of cube to the volume of cylinder = \(\frac{4}{ᴨ}\)

Hence, the correct answer is Option C

Answer: C

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Re: If the radius of a cylinder is half the length of the edge of a cube,  [#permalink]

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New post 15 Nov 2018, 04:36
Bunuel 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. \(\frac{2}{\pi}\)

B. \(\frac{\pi}{4}\)

C. \(\frac{4}{\pi}\)

D. \(\frac{\pi}{2}\)

E. 4


Let side of cube be 2

So radius will be 1 and height will be 2

Volume of cube = s^3 = 2^3 = 8

Volume of cylinder = pi r^2 * h = pi * 1 * 2

8/(2*pi) = 4/pi

Answer choice C

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Re: If the radius of a cylinder is half the length of the edge of a cube,  [#permalink]

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New post 15 Nov 2018, 04:50
Bunuel 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. \(\frac{2}{\pi}\)

B. \(\frac{\pi}{4}\)

C. \(\frac{4}{\pi}\)

D. \(\frac{\pi}{2}\)

E. 4



Let edge of cube be 4, so radius of cylinder is 2 and height is 4.

using given relation we find ratio to be = 4*4*4/pi*2*2*4 = answer option C
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Re: If the radius of a cylinder is half the length of the edge of a cube,  [#permalink]

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New post 13 Apr 2019, 18:40
Bunuel 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. \(\frac{2}{\pi}\)

B. \(\frac{\pi}{4}\)

C. \(\frac{4}{\pi}\)

D. \(\frac{\pi}{2}\)

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 = πr^2h, the volume of the cylinder is:

V = π(x/2)^2 * x

V = π(x^2/4) * x

V = x^3 * π/4

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

x^3/(x^3 * π/4)

1/(π/4)

4/π

Answer: C
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Re: If the radius of a cylinder is half the length of the edge of a cube,   [#permalink] 13 Apr 2019, 18:40
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