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18 Jun 2019, 00:35
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
44% (03:07) correct
56%
(03:36)
wrong
based on 64
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A right cylinder and a cube have the same surface area. If the height of the cylinder is equal to its diameter, then the volume of the cylinder is approximately what percent greater than the volume of the cube?
A. 6%
B. 13%
C. 26%
D. 32%
E. 35%
A. 6%
B. 13%
C. 26%
D. 32%
E. 35%
18 Jun 2019, 11:34
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Bunuel
Given, h = 2r
Let r = 1, h = 2
Surface area of cylinder = 2πr(h + r)
= 2πr(2r + r) = 6π
Surface area of cube = 6a^2
A right cylinder and a cube have the same surface area
—> 6π = 6a^2
—> a^2 = π
—> a = √π
% greater = (volume of cylinder - volume of cube)/volume of cube*100
= (πr^2h - a^3)/a^3*100
= (2π - π√π)/π√π*100
= (2/√π - 1)*100
= (2/√3.14 - 1)*100
= 13%
IMO Option B
Pls Hit kudos if you like the solution
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23 Jun 2019, 19:33
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Bunuel
We can let d = the diameter (or height) of the cylinder. Since the surface area of a cylinder is 2πrh + 2πr^2, the surface area of this cylinder is 2π(d/2)(d) + 2π(d/2)^2 = πd^2 + πd^2/2 = 3πd^2/2.
Since the cube has the same surface area and the surface area of a cube is 6s^2, we have:
6s^2 = 3πd^2/2
s^2 = πd^2/4
s = (√π)d/2
Since the volume of a cylinder is πr^2h, the volume of this cylinder is π(d/2)^2*d = πd^3/4. Since the volume of a cube is s^3, the volume of this cube is [(√π)d/2]^3 = (π√π)d^3/8. Therefore, the volume of the cylinder is:
(πd^3/4)/[(π√π)d^3/8] = (1/4)/(√π/8) = 2/√π ≈ 1.13 times the volume of the cube.
In other words, the volume of the cylinder is approximately 13% greater than the volume of the cube.
Answer: B
