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03 May 2018, 05:48
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
87% (01:41) correct
13%
(01:28)
wrong
based on 52
sessions
History
Date
Time
Result
Not Attempted Yet
A cylinder with a volume of \(54\pi\) has the same height and diameter. What is its diameter?
A) 6
B) 9
C) 12
D) 18
E) 24
A) 6
B) 9
C) 12
D) 18
E) 24
03 May 2018, 05:48
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Official solution:
Area: \(\pi\)\((r)^{2}*height = 54\pi\)
Since diameter \(=\) \(2r\)\(= height\), then \(r = \frac{1}{2}d = \frac{1}{2}h\)
Therefore, Area \(=\) \(\pi(\frac{1}{2} h)^{2} *h= 54\pi\) -> Area \(=\) \(\pi (\frac{h^{2}}{4})*h = 54\pi\)
Area \(=\) \(\pi (\frac{h^{3}}{4}) = 54\pi\) -> Area \(=\) \(h^{3} = 216\) -> \(h = 6 = d = 6\)
Area: \(\pi\)\((r)^{2}*height = 54\pi\)
Since diameter \(=\) \(2r\)\(= height\), then \(r = \frac{1}{2}d = \frac{1}{2}h\)
Therefore, Area \(=\) \(\pi(\frac{1}{2} h)^{2} *h= 54\pi\) -> Area \(=\) \(\pi (\frac{h^{2}}{4})*h = 54\pi\)
Area \(=\) \(\pi (\frac{h^{3}}{4}) = 54\pi\) -> Area \(=\) \(h^{3} = 216\) -> \(h = 6 = d = 6\)
03 May 2018, 09:44
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fallenx
Kinda too messy solution for the prep company (by the way Area and Volume are different things)
V=\(\pi\)\((r)^{2}*h = 54\pi\), where
\(h=d=2r\)
\(\pi\)\((r)^{2}*2r= 54\pi\)
\(r=3,d=6\). Answer (A)
