Question

The curved surface area of a cylinder is reduced by ____________ per cent if the height is half of the original height.

Answer 1

Step- 1: cylinder surface area:

Cylinder is one of the basic $\text{3D}$ shapes, in geometry, which has two parallel circular bases at a distance.The two circular bases are joined by a curved surface, at a fixed distance from the centre

If $h=$ Height of the cylinder and $r=$ Radius of the cylinder

Then $\text{C.S.A}$ of cylinder $=2\mathrm{\pi rh}$

Step- 2: Percentage reduction:

According to question When the height is halved

Then new $C.S.A$$=2\mathrm{\pi r}\frac{\mathrm{h}}{2}=\mathrm{\pi rh}$

Therefore, the percentage reduction in $C.S.A=\frac{\text{change in}C.S.A}{\text{origional}C.S.A}x100$

$$\begin{gathered} =\frac{2\mathrm{\pi rh}-\mathrm{\pi rh}}{2\mathrm{\pi rh}}x100 \\ =\frac{\mathrm{\pi rh}}{2\mathrm{\pi rh}}x100 \\ =50\% \end{gathered}$$

Hence, the curved surface area of a cylinder is reduced by $50\%$.