The curved surface area of a cylindrical pillar is 264 m

Question:

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and height of the pillar.

Solution:

Curved surface area $=2 \pi \mathrm{rh}=264 \mathrm{~m}^{2}$

$\therefore r=\frac{264}{2 \pi \mathrm{h}}=\frac{132}{\pi \mathrm{h}} m$

Volume $=\pi \mathrm{r}^{2} \mathrm{~h}=\pi \times \frac{132}{\pi \mathrm{h}} \times \frac{132}{\pi \mathrm{h}} \times \mathrm{h}=924 \mathrm{~m}^{3}$

$\therefore h=\frac{132 \times 132 \times 7}{22 \times 924}=6 \mathrm{~m}$

Now, $r=\frac{132}{\pi \mathrm{h}}=\frac{132 \times 7}{22 \times 6}=7 m$

i.e., diameter of the pillar, $d=7 \times 2=14 \mathrm{~m}$

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