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A 12 feet high sand mound is in the shape of a circular cylinder. If t
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07 Aug 2025, 09:17
07 Aug 2025, 09:17
Expert Reply
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Question Stats:
50% (02:36) correct
50% (02:40) wrong based on 2 sessions
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A 12 feet high sand mound is in the shape of a circular cylinder. If the volume of the sand in the mound is $96 \pi$, what is the area enclosed by the base of the mound?
(A) $\(\frac{156}{7}\)$
(B) $\(\frac{160}{7}\)$
(C) $\(\frac{167}{7}\)$
(D) $\(\frac{176}{7}\)$
(E) $\(\frac{276}{7}\)$
(A) $\(\frac{156}{7}\)$
(B) $\(\frac{160}{7}\)$
(C) $\(\frac{167}{7}\)$
(D) $\(\frac{176}{7}\)$
(E) $\(\frac{276}{7}\)$
Re: A 12 feet high sand mound is in the shape of a circular cylinder. If t
[#permalink]
20 Aug 2025, 03:50
20 Aug 2025, 03:50
Expert Reply
Given:
- Height $\((\mathrm{h})\)$ of the circular cylinder $\(=12\)$ feet.
- Volume of the cylinder $=96 \pi$.
Volume of a cylinder formula:
$$
\(V=\text { Base Area } \times h\),
$$
where Base Area $\(=\pi r^2\)$.
We want to find the base area, so:
$$
\(\text { Base Area }=\frac{V}{h}=\frac{96 \pi}{12}=8 \pi \).
$$
Since base area is $\(\pi r^2\)$, here it equals $8 \pi$ :
$$
\(\pi r^2=8 \pi \Longrightarrow r^2=8\)
$$
Area enclosed by the base is $\(\pi r^2=8 \pi\)$.
We need to find the equivalent value in the options given in fraction form with denominator 7.
Using $\(\pi=\frac{22}{7}\)$ :
$$
\(8 \pi=8 \times \frac{22}{7}=\frac{176}{7}\)
$$
Answer is (D) $\(\frac{176}{7}\)$. The area enclosed by the base of the mound is $\(\frac{176}{7}\)$.
- Height $\((\mathrm{h})\)$ of the circular cylinder $\(=12\)$ feet.
- Volume of the cylinder $=96 \pi$.
Volume of a cylinder formula:
$$
\(V=\text { Base Area } \times h\),
$$
where Base Area $\(=\pi r^2\)$.
We want to find the base area, so:
$$
\(\text { Base Area }=\frac{V}{h}=\frac{96 \pi}{12}=8 \pi \).
$$
Since base area is $\(\pi r^2\)$, here it equals $8 \pi$ :
$$
\(\pi r^2=8 \pi \Longrightarrow r^2=8\)
$$
Area enclosed by the base is $\(\pi r^2=8 \pi\)$.
We need to find the equivalent value in the options given in fraction form with denominator 7.
Using $\(\pi=\frac{22}{7}\)$ :
$$
\(8 \pi=8 \times \frac{22}{7}=\frac{176}{7}\)
$$
Answer is (D) $\(\frac{176}{7}\)$. The area enclosed by the base of the mound is $\(\frac{176}{7}\)$.
gmatclubot
Re: A 12 feet high sand mound is in the shape of a circular cylinder. If t [#permalink]
20 Aug 2025, 03:50
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