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The radius of a cylindrical tank is 28m. If its capacity is equal to that of a rectangular tank of size 28mx16mx11m, then its depth is
- a)4 m
- b)3 m
- c)5 m
- d)2 m
Correct answer is option 'B'. Can you explain this answer?
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To find the depth of the cylindrical tank, we need to compare its capacity with that of the rectangular tank.
Capacity of a cylindrical tank = πr^2h
Capacity of a rectangular tank = lwh
Given:
Radius of the cylindrical tank (r) = 28m
Length of the rectangular tank (l) = 28m
Width of the rectangular tank (w) = 16m
Height of the rectangular tank (h) = 11m
Let's calculate the capacity of the cylindrical tank first.
Capacity of the cylindrical tank = π(28)^2h
Capacity of the cylindrical tank = 784πh
Now, let's calculate the capacity of the rectangular tank.
Capacity of the rectangular tank = lwh
Capacity of the rectangular tank = 28 * 16 * 11
Capacity of the rectangular tank = 4928
Since the capacities of both tanks are equal, we can equate the two expressions:
784πh = 4928
Now, let's solve for h (the depth of the cylindrical tank).
784πh = 4928
h = 4928 / (784π)
h = 1.972 / π
h ≈ 0.628
Therefore, the depth of the cylindrical tank is approximately 0.628m, which is closest to 2m (option D).
So, the correct answer is option D.
Capacity of a cylindrical tank = πr^2h
Capacity of a rectangular tank = lwh
Given:
Radius of the cylindrical tank (r) = 28m
Length of the rectangular tank (l) = 28m
Width of the rectangular tank (w) = 16m
Height of the rectangular tank (h) = 11m
Let's calculate the capacity of the cylindrical tank first.
Capacity of the cylindrical tank = π(28)^2h
Capacity of the cylindrical tank = 784πh
Now, let's calculate the capacity of the rectangular tank.
Capacity of the rectangular tank = lwh
Capacity of the rectangular tank = 28 * 16 * 11
Capacity of the rectangular tank = 4928
Since the capacities of both tanks are equal, we can equate the two expressions:
784πh = 4928
Now, let's solve for h (the depth of the cylindrical tank).
784πh = 4928
h = 4928 / (784π)
h = 1.972 / π
h ≈ 0.628
Therefore, the depth of the cylindrical tank is approximately 0.628m, which is closest to 2m (option D).
So, the correct answer is option D.
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The radius of a cylindrical tank is 28m. If its capacity is equal to that of a rectangular tank of size 28mx16mx11m, then its depth isa)4 mb)3 mc)5 md)2 mCorrect answer is option 'B'. Can you explain this answer?
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