Question : If the radius of a right circular cylinder open at both ends is decreased by 25% and the height of the cylinder is increased by 25%, the curved surface area of the cylinder thus formed:
Option 1: remains unaltered
Option 2: is increased by $25\%$
Option 3: is increased by $6.25\%$
Option 4: is decreased by $6.25\%$
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Correct Answer: is decreased by $6.25\%$
Solution : The curved surface area of a right circular cylinder before the change, where $r$ is the radius and $h$ is the height $ = 2\pi rh$ The radius is decreased by $25\%$, $r' = 0.75r$ The height is increased by $25\%$, $h' = 1.25h$ The curved surface area of a right circular cylinder after the change $= 2\pi r' h' = 2\pi (0.75r)(1.25h) = 2\pi rh × 0.75 × 1.25 =1.875\pi rh$ $\therefore$ Percentage change = $(\frac{2\pi rh-1.875\pi rh}{2\pi rh})×100= 6.25\%$ Hence, the correct answer is 'is decreased by $6.25\%$'.
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Question : The curved surface area of a right circular cylinder of height 56 cm is 1408 cm². Find the diameter of the base of the cylinder.
Option 1: 8 m
Option 2: 0.04 m
Option 3: 0.08 m
Option 4: 0.008 m
Question : The curved surface area of a cylinder is five times the area of its base. Find the ratio of the radius and height of the cylinder.
Option 1: 2 : 3
Option 2: 3 : 5
Option 3: 2 : 5
Option 4: 3 : 4
Question : If the radius of a cylinder is increased by 25%, by how much percentage the height must be reduced, so that the volume of the cylinder remains the same.
Option 1: 36
Option 2: 56
Option 3: 64
Option 4: 46
Question : If the numerical value of twice the curved surface area of a right circular cylinder is equal to the numerical value of its volume, then what is the numerical value of the radius of the base of the cylinder?
Option 1: 2
Option 2: 3
Option 3: 5
Option 4: 4
Question : If the radius of a cylinder is decreased by 20% and the height is increased by 20% to form a new cylinder, then the volume will be decreased by:
Option 1: 23.2%
Option 2: 22.3%
Option 3: 32.2%
Option 4: 20.5%
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