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The volume of a pyramid varies jointly as its height and the area of its base; and when the area of the base is 60 square dm and the height 14 dm, the volume is 280 cubic dm. What is the area of the base of a pyramid whose volume is 390 cubic dm and whose height is 26 dm?
- a)40
- b)50
- c)45
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The volume of a pyramid varies jointly as its height and the area of i...
V = k AH -> 280 = k X 60 X 14
⇒ 280 = 840k.
Thus, k = 1 / 3 and the equation becomes
⇒ 280 = 840k.
Thus, k = 1 / 3 and the equation becomes
V = AH / 3 and 390 = 26A / 3 -> A = 45.
Most Upvoted Answer
The volume of a pyramid varies jointly as its height and the area of i...
To solve this problem, we can use the concept of variation. Let's denote the volume of the pyramid as V, the height as h, and the area of the base as A.
According to the given information, the volume of the pyramid varies jointly as its height and the area of its base. This can be expressed as:
V ∝ h * A
We can rewrite this as an equation by introducing a constant of variation, k:
V = k * h * A
We are given that when the area of the base is 60 square dm and the height is 14 dm, the volume is 280 cubic dm. Substituting these values into the equation, we get:
280 = k * 14 * 60
Simplifying the equation, we find:
k = 280 / (14 * 60) = 1/3
Now we can use this value of k to find the area of the base when the volume is 390 cubic dm and the height is 26 dm. Substituting these values into the equation, we get:
390 = (1/3) * 26 * A
Simplifying the equation, we find:
A = (3 * 390) / (26) = 45 square dm
Therefore, the area of the base of the pyramid whose volume is 390 cubic dm and whose height is 26 dm is 45 square dm.
Hence, the correct answer is option C) 45.
According to the given information, the volume of the pyramid varies jointly as its height and the area of its base. This can be expressed as:
V ∝ h * A
We can rewrite this as an equation by introducing a constant of variation, k:
V = k * h * A
We are given that when the area of the base is 60 square dm and the height is 14 dm, the volume is 280 cubic dm. Substituting these values into the equation, we get:
280 = k * 14 * 60
Simplifying the equation, we find:
k = 280 / (14 * 60) = 1/3
Now we can use this value of k to find the area of the base when the volume is 390 cubic dm and the height is 26 dm. Substituting these values into the equation, we get:
390 = (1/3) * 26 * A
Simplifying the equation, we find:
A = (3 * 390) / (26) = 45 square dm
Therefore, the area of the base of the pyramid whose volume is 390 cubic dm and whose height is 26 dm is 45 square dm.
Hence, the correct answer is option C) 45.
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Community Answer
The volume of a pyramid varies jointly as its height and the area of i...
V = k AH -> 280 = k X 60 X 14
⇒ 280 = 840k.
Thus, k = 1 / 3 and the equation becomes
⇒ 280 = 840k.
Thus, k = 1 / 3 and the equation becomes
V = AH / 3 and 390 = 26A / 3 -> A = 45.
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The volume of a pyramid varies jointly as its height and the area of its base; and when the area of the base is 60 square dm and the height 14 dm, the volume is 280 cubic dm. What is the area of the base of a pyramid whose volume is 390 cubic dm and whose height is 26 dm?a)40b)50c)45d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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