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A metallic cylinder of diameter 14 units and height 98 units is cast i
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03 May 2025, 09:13
03 May 2025, 09:13
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Question Stats:
66% (02:41) correct
33% (02:51) wrong based on 3 sessions
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A metallic cylinder of diameter 14 units and height 98 units is cast into hemispherical bowls with outer radius 14 units and thickness 7 units. How many bowls can be drawn from the cylinder?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 14
(A) 2
(B) 3
(C) 5
(D) 7
(E) 14
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Re: A metallic cylinder of diameter 14 units and height 98 units is cast i
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08 May 2025, 04:15
08 May 2025, 04:15
Expert Reply
The volume of each bowl $\(=\frac{1}{2} \times \frac{4}{3} \pi\left(r_2^2-r_1^2\right)=\frac{4}{3} \frac{\pi\left(14^3-7^3\right)}{2}\)$ and
The volume of the cylinder $\(\left(\pi r^2 h\right)=\pi \times 7^2 \times 98\)$.
Therefore, the number of bowls that can be drawn from the cylinder $\(=\frac{\pi \times 49 \times 98 \times 3 \times 2}{4 \times \pi \times 2401}=3\)$.
Thus, the correct answer is $\(B\)$.
The volume of the cylinder $\(\left(\pi r^2 h\right)=\pi \times 7^2 \times 98\)$.
Therefore, the number of bowls that can be drawn from the cylinder $\(=\frac{\pi \times 49 \times 98 \times 3 \times 2}{4 \times \pi \times 2401}=3\)$.
Thus, the correct answer is $\(B\)$.
gmatclubot
Re: A metallic cylinder of diameter 14 units and height 98 units is cast i [#permalink]
08 May 2025, 04:15
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