Question

A solid cylinder of radius$r$and height $h$ is placed over other cylinder of same height and radius. The total surface area of the shape so formed is $4\mathrm{\pi rh}+4{\mathrm{\pi r}}^2$.

• A. True
• B. False

Answer 1

The correct option is B False

According to the given data

When one cylinder is placed over another, the base of first cylinder and top of other cylinder will not be covered in total surface area.

We know that,

Total surface area of cylinder $=2\mathrm{\pi rh}+2{\mathrm{\pi r}}^2\mathrm{h}$,

where

$r=$ base radius

$h=$ height

Total surface area of shape formed$=$$2$(Total surface of single cylinder) $-2$(Area of base of cylinder)

$$\begin{gathered} =2(2\mathrm{\pi rh}+2{\mathrm{\pi r}}^2)-2{\mathrm{\pi r}}^2 \\ =4\mathrm{\pi rh}+2{\mathrm{\pi r}}^2 \end{gathered}$$

Hence, statement is false.