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If the ratio between radius and height of the cylinder is 4 ∶ 5. Now, if the radius of cylinder is increased by 20% and the height of the cylinder is decreased by 10% then find how many percent increase in volume of cylinder.
- a)30%
- b)28.5%
- c)29.6%
- d)15%
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the ratio between radius and height of the cylinder is 4 ∶ 5. Now,...
Ratio between radius and height = 4 ∶ 5
Radius of the cylinder = r = 4x
Height of the cylinder = h = 5x
Volume of the cylinder = πr2h
⇒ π(4x)2(5x)
⇒ π × 16x2 × 5x
⇒ 80πx3
Radius increased by 20%
Increase in the radius = 4x × 20/100 = 4x/5
∴ Increased radius = R = 4x + 4x/5 = 24x/5
Height decreased by 10%
Decrease in the height = 5x × (10/100) = x/2
∴ Decreased height = H = 5x – (x/2) = 9x/2
New volume of the cylinder = πR2H
Change in the volume of the cylinder = New volume of the cylinder – Volume of the cylinder
Percentage increase in volume of the cylinder
∴ Percentage Increase in volume of the cylinder = 29.6%
Hence, the correct option is (C).
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If the ratio between radius and height of the cylinder is 4 ∶ 5. Now,...
To find the percentage increase in volume of the cylinder after the given changes in the dimensions, we need to follow these steps:
Step 1: Initial Ratio of Radius to Height
Given that the ratio between the radius and height of the cylinder is 4:5.
Step 2: Initial Volume of the Cylinder
Let the initial radius be 4x and the initial height be 5x. The initial volume of the cylinder is π(4x)^2 * 5x = 80πx^3.
Step 3: New Dimensions
After increasing the radius by 20%, the new radius becomes 1.2 * 4x = 4.8x. After decreasing the height by 10%, the new height becomes 0.9 * 5x = 4.5x.
Step 4: New Volume of the Cylinder
The new volume of the cylinder is π(4.8x)^2 * 4.5x = 103.68πx^3.
Step 5: Percentage Increase in Volume
The percentage increase in volume is calculated as [(New Volume - Initial Volume) / Initial Volume] * 100%.
Substitute the values to get [(103.68πx^3 - 80πx^3) / 80πx^3] * 100% = 29.6%.
Therefore, the percentage increase in volume of the cylinder is 29.6%. Hence, the correct answer is option (c) 29.6%.
Step 1: Initial Ratio of Radius to Height
Given that the ratio between the radius and height of the cylinder is 4:5.
Step 2: Initial Volume of the Cylinder
Let the initial radius be 4x and the initial height be 5x. The initial volume of the cylinder is π(4x)^2 * 5x = 80πx^3.
Step 3: New Dimensions
After increasing the radius by 20%, the new radius becomes 1.2 * 4x = 4.8x. After decreasing the height by 10%, the new height becomes 0.9 * 5x = 4.5x.
Step 4: New Volume of the Cylinder
The new volume of the cylinder is π(4.8x)^2 * 4.5x = 103.68πx^3.
Step 5: Percentage Increase in Volume
The percentage increase in volume is calculated as [(New Volume - Initial Volume) / Initial Volume] * 100%.
Substitute the values to get [(103.68πx^3 - 80πx^3) / 80πx^3] * 100% = 29.6%.
Therefore, the percentage increase in volume of the cylinder is 29.6%. Hence, the correct answer is option (c) 29.6%.
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