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If the curved surface area of a cylindrical pillar is 264m² and it's volume is 924m³, then find the height and diameter
Given :
The curved surface area of a cylindrical pillar is $264\ m^2$ and its volume is $924\ m^3$.
To do:
We have to find the height and diameter.
Solution:
Let the radius of the base of the cylinder be $r$ and the height be $h$.
The curved surface area of a cylinder of radius r and height $h = 2\pi rh$
Therefore,
$2\pi rh= 2 \times \frac{22}{7} \times r \times h$
$264(7) = 44rh$
$h=\frac{42}{r}\ m$.....(i)
Volume of the cylinder $=\pi r^2h$
$924=\frac{22}{7} \times r^2 \times \frac{42}{r}$ [From (i)]
$42=6r$
$r=\frac{42}{6}$
$r=7\ m$
This implies,
$h=\frac{42}{7}\ m$
$h=6\ m$
Diameter$=2r=2(7)\ m=14\ m$.
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