Write ‘True’ or ‘False’ and justify your answer in the following:… - Vidyadip

Question

Write ‘True’ or ‘False’ and justify your answer in the following:
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 $4\pi\text{r h}+4\pi\text{r}^2.$

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Answer

False: When two identical cylinders of same radius 'r' and height 'h' are stuck base (circular) to base, then the resulting cylinder will have h' = 2h, r' = r
$\therefore\ \ \text{T.S.A}=2\pi\text{r}'(\text{r}'+\text{h})=2\pi\text{r}(\text{r}+2\text{h})=2\pi\text{r}^2+2\pi\text{r}.2\text{h}$
$=4\pi\text{r h}+2\pi\text{r}^2$
Hence, the given statement is false.

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