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The ratio of the volume of a cone to the volume of a cylinder of the s
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05 May 2025, 02:53
05 May 2025, 02:53
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Question Stats:
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The ratio of the volume of a cone to the volume of a cylinder of the same height is $1: 3$. If the diameter of cone is 6 cm , what is the radius (in cm ) of the cylinder?
(A) 2
(B) 3
(C) 6
(D) 9
(E) 18
(A) 2
(B) 3
(C) 6
(D) 9
(E) 18
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Re: The ratio of the volume of a cone to the volume of a cylinder of the s
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08 May 2025, 04:00
08 May 2025, 04:00
Expert Reply
\(\begin{aligned}
&\begin{aligned}
& V_{c o n e}=\frac{1}{3} \pi r_1^2 h \text { and } V_{c y l}=\pi r_2^2 h \\
& \frac{V_{c o n}}{V_{c y l}}=\frac{r_1^2}{3 r_2^2}=\frac{1}{3} \cdot 2 r_1=6 . \Rightarrow r_1=3 \Rightarrow 3^2 \times 3=r_2^2 \cdot 3 \Rightarrow r_2=3 .
\end{aligned}\\
&\text { Thus, the correct answer is } B \text {. }
\end{aligned}\)
&\begin{aligned}
& V_{c o n e}=\frac{1}{3} \pi r_1^2 h \text { and } V_{c y l}=\pi r_2^2 h \\
& \frac{V_{c o n}}{V_{c y l}}=\frac{r_1^2}{3 r_2^2}=\frac{1}{3} \cdot 2 r_1=6 . \Rightarrow r_1=3 \Rightarrow 3^2 \times 3=r_2^2 \cdot 3 \Rightarrow r_2=3 .
\end{aligned}\\
&\text { Thus, the correct answer is } B \text {. }
\end{aligned}\)
gmatclubot
Re: The ratio of the volume of a cone to the volume of a cylinder of the s [#permalink]
08 May 2025, 04:00
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