Question
From a solid cylinder whose height is $15\ cm$ and diameter $16\ cm$, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. $[$Use $\pi= 3.14]$
✓
Answer
We have,
Height of the cylinder $=$ Height of the cone $= h = 15\ cm$ and
Radius of the cylinder $=$ Radius of the cone $\text{r}=\frac{16}{2}=8\text{cm}$
Also, the slant height of the cone, $\text{l}=\sqrt{\text{h}^2+\text{r}^2}$
$=\sqrt{15^2+8^2}$
$=\sqrt{225+64}$
$=\sqrt{289}$
$=17\text{cm}$
Now,
The total surface area of the remaining solid $= CSA $of the cone $+ CSA$ of the cylinder $+$ Are of the base
$=\pi\text{r}\text{l}+2\pi\text{rh}+\pi\text{r}^2$
$=\pi\text{r}(\text{l}+2\text{h}+\text{r})$
$=3.14\times8\times(17+2\times15+8)$
$=3.14\times8\times55$
$=1381.6\text{cm}^2$
So, the total surface area of the remaining solid is $1381.6\ cm^2.$
Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.
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