Question

# In a cylinder, if radius is doubled and height is halved, curved surface area will be _________.

Solution

## Let r and h be the radius and height of the cylinder, respectively. ∴ Curved surface of the original cylinder, C1 = 2$\mathrm{\pi }$rh  If the radius is doubled and height is halved, then Radius of the new cylinder, R = 2r Height of the new cylinder, H = $\frac{h}{2}$ ∴ Curved surface of the new cylinder, C2 = $2\mathrm{\pi }RH=2\mathrm{\pi }×2r×\frac{h}{2}$ = 2$\mathrm{\pi }$rh Thus, the curved surface area of the new cylinder is same as the curved surface area of the original cylinder. In a cylinder, if radius is doubled and height is halved, curved surface area will be __same__.MathematicsRD Sharma (2019)All

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