Cylinder Volume Calculation

This solution explains how to find the volume of a cylinder when its height and curved surface area are known.

Given Information

• Height of the cylinder, $h = 14$ cm.
• Curved Surface Area (CSA) of the cylinder = $264$ cm².
• The value of pi ($\pi$) is given as $\frac{22}{7}$.

Finding the Radius of the Cylinder

The formula for the curved surface area (CSA) of a cylinder is:

$ \text{CSA} = 2 \pi r h $

Where '$r$' is the radius and '$h$' is the height.

We are given CSA = $264$ cm² and $h = 14$ cm. We can substitute these values into the formula to find the radius '$r$':

$ 264 = 2 \times \frac{22}{7} \times r \times 14 $

Simplify the equation:

$ 264 = 2 \times 22 \times r \times \frac{14}{7} $

$ 264 = 2 \times 22 \times r \times 2 $

$ 264 = 88 \times r $

Now, solve for '$r$':

$ r = \frac{264}{88} $

$ r = 3 $

So, the radius of the cylinder is $3$ cm.

Calculating the Volume of the Cylinder

The formula for the volume ($V$) of a cylinder is:

$ V = \pi r^2 h $

Now substitute the values of $\pi$, the calculated radius ($r=3$ cm), and the given height ($h=14$ cm) into the volume formula:

$ V = \frac{22}{7} \times (3 \text{ cm})^2 \times 14 \text{ cm} $

$ V = \frac{22}{7} \times 9 \text{ cm}^2 \times 14 \text{ cm} $

Simplify the calculation:

$ V = 22 \times 9 \times \frac{14}{7} \text{ cm}^3 $

$ V = 22 \times 9 \times 2 \text{ cm}^3 $

$ V = 22 \times 18 \text{ cm}^3 $

$ V = 396 \text{ cm}^3 $

Conclusion

Therefore, the volume of the cylinder is calculated to be $396$ cm³.