The curved surface area of a cylindrical pillar is $66\text{ m}^2$ and its volume is $231\text{ m}^3$. Find the measure of its radius. $(\text{Take } \pi = \frac{22}{7})$
Calculating Cylindrical Pillar Radius
We are given the following information for a cylindrical pillar:
- Curved Surface Area ($CSA$) = $66\text{ m}^2$
- Volume ($V$) = $231\text{ m}^3$
- Value of $\pi$ to be used = $\frac{22}{7}$
We need to find the radius ($r$) of the pillar.
Cylinder Formulas
The standard formulas for a cylinder are:
- Curved Surface Area: $CSA = 2\pi rh$
- Volume: $V = \pi r^2 h$
Where '$r$' is the radius and '$h$' is the height.
Deriving Radius
To find the radius, we can divide the volume formula by the curved surface area formula. This helps eliminate the height ($h$):
$ \frac{V}{CSA} = \frac{\pi r^2 h}{2\pi rh} $Simplifying the equation:
$ \frac{V}{CSA} = \frac{r}{2} $Solving for Radius
Now, substitute the given values into the derived formula:
$ \frac{231\text{ m}^3}{66\text{ m}^2} = \frac{r}{2} $Simplify the fraction on the left side. Both 231 and 66 are divisible by 33 (or sequentially by 3 and 11):
$ \frac{231 \div 33}{66 \div 33} = \frac{7}{2} $So, the equation becomes:
$ \frac{7}{2} = \frac{r}{2} $Multiplying both sides by 2 to solve for '$r$':
$ r = 7 $Therefore, the radius of the cylindrical pillar is $7\text{ m}$.
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