Question

The curved surface area of a cylinder is \(264\ m^2\) and its volume is \(924\ m^3\) then height of the cylinder is

• A. 3 m
• B. 8 m
• C. 6 m
• D. 4 m

Answer 1

The Correct Option is C

To solve the problem, we are given:

• Curved Surface Area (CSA) of the cylinder = 264 m²
• Volume of the cylinder = 924 m³

1. Formulas to Use:
- Curved Surface Area of a cylinder: $ \text{CSA} = 2\pi rh $
- Volume of a cylinder: $ V = \pi r^2 h $

2. Use CSA to Find Radius in Terms of Height:

From $2\pi rh = 264$

Divide both sides by $2\pi$:

$ rh = \frac{264}{2\pi} = \frac{132}{\pi} $         (Equation 1)

3. Use Volume Formula:

$ \pi r^2 h = 924 $

Substitute $rh$ from Equation 1:

Multiply both sides of Equation 1 by $r$:

$ r \cdot rh = r \cdot \frac{132}{\pi} \Rightarrow r^2 h = \frac{132r}{\pi} $
So:
$ \pi \cdot r^2 h = 132r = 924 $
Now solve for $r$:
$ 132r = 924 \Rightarrow r = \frac{924}{132} = 7 $

4. Substitute $r = 7$ in Equation 1 to Get Height:

$ rh = \frac{132}{\pi} \Rightarrow 7h = \frac{132}{\pi} $

$ h = \frac{132}{7\pi} $

Use $ \pi \approx 3.14 $:

$ h = \frac{132}{7 \times 3.14} = \frac{132}{21.98} \approx 6 $

Final Answer:
The height of the cylinder is $ {6 \, \text{m}} $.