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The volume of a pyramid varies directly
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30 Apr 2026, 04:14
30 Apr 2026, 04:14
Expert Reply
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Question Stats:
63% (01:39) correct
36% (01:17) wrong based on 11 sessions
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The volume of a pyramid varies directly jointly with its height and the area of its base. A pyramid with a height of 12 feet and a base with an area of 23 square feet has a volume of 92 cubic feet. Find the volume, in cubic feet, of a pyramid with a height of 13 feet and a base with an area of 24 square feet.
A. 48
B 104
C. 192
D. 276
E. 312
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A. 48
B 104
C. 192
D. 276
E. 312
Please, subscribe to the TTP - Question of the day here https://gre.targettestprep.com/question_of_the_day
Re: The volume of a pyramid varies directly
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01 May 2026, 07:25
01 May 2026, 07:25
1
The volume varies directly jointly with height and base area.
That means:
Volume = constant × height × base area
So:
V = k × h × A
We are given:
V = 92
h = 12
A = 23
So:
92 = k × 12 × 23
Divide both sides by 23:
4 = 12k
--> k = 1/3
Therefore, the formula is:
V = (1/3) × h × A
Now use the new values:
h = 13
A = 24
V = (1/3) × 13 × 24
V = 13 × 8
V = 104
The answer is B.
That means:
Volume = constant × height × base area
So:
V = k × h × A
We are given:
V = 92
h = 12
A = 23
So:
92 = k × 12 × 23
Divide both sides by 23:
4 = 12k
--> k = 1/3
Therefore, the formula is:
V = (1/3) × h × A
Now use the new values:
h = 13
A = 24
V = (1/3) × 13 × 24
V = 13 × 8
V = 104
The answer is B.
General Discussion
Re: The volume of a pyramid varies directly
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06 May 2026, 04:15
06 May 2026, 04:15
Expert Reply
We can let \(\mathrm{V}, \mathrm{h}\), and A represent the volume, height, and base area of the pyramid, respectively. Because V varies directly jointly with h and A, we can set up a joint variation equation \(\mathrm{V}=\mathrm{khA}\), where k is some unknown constant. Substituting the initial given values for \(\mathrm{V}, \mathrm{h}\), and A , we can solve for k .
\(\begin{aligned}
& \Rightarrow \mathrm{V}=\mathrm{khA} \\
& \Rightarrow 92=\mathrm{k}(12)(23) \\
& \Rightarrow \frac{92}{276}=\mathrm{k} \\
& \Rightarrow \frac{1}{3}=\mathrm{k}
\end{aligned}\)
Now that we know the value of k in a pyramid's volume equation, we can determine V when \(\mathrm{h}=13\) and \(\mathrm{A}=24\).
\(\begin{aligned}
& \Rightarrow V=\frac{1}{3} h A \\
& \Rightarrow V=\frac{1}{3}(13)(24) \\
& \Rightarrow V=104
\end{aligned}\)
The volume of the pyramid is 104 cubic feet.
\(\begin{aligned}
& \Rightarrow \mathrm{V}=\mathrm{khA} \\
& \Rightarrow 92=\mathrm{k}(12)(23) \\
& \Rightarrow \frac{92}{276}=\mathrm{k} \\
& \Rightarrow \frac{1}{3}=\mathrm{k}
\end{aligned}\)
Now that we know the value of k in a pyramid's volume equation, we can determine V when \(\mathrm{h}=13\) and \(\mathrm{A}=24\).
\(\begin{aligned}
& \Rightarrow V=\frac{1}{3} h A \\
& \Rightarrow V=\frac{1}{3}(13)(24) \\
& \Rightarrow V=104
\end{aligned}\)
The volume of the pyramid is 104 cubic feet.
