Question

The ratio of diameter to its height of a cylindrical pillar is 7 : 3. The volume of the pillar is 924 m\(^3\). Its curved surface area is .......

• A. 306 m\(^2\)
• B. 264 m\(^2\)
• C. 384 m\(^2\)
• D. 456 m\(^2\)

Hint:

In problems involving volumes and surface areas of cylinders, make sure to convert the diameter to the radius and use the appropriate formulas for both volume and surface area.

Answer 1

The Correct Option is B

Let the height of the cylindrical pillar be \( h = 3x \) and the diameter of the pillar be \( d = 7x \). So, the radius \( r \) will be \( r = \frac{d}{2} = \frac{7x}{2} \). Step 1: Volume of the cylinder. The formula for the volume of the cylinder is: \[ V = \pi r^2 h \] Substitute the values for \( r \) and \( h \): \[ 924 = \pi \left( \frac{7x}{2} \right)^2 \times 3x \] \[ 924 = \pi \times \frac{49x^2}{4} \times 3x \] \[ 924 = \pi \times \frac{147x^3}{4} \] \[ x^3 = \frac{924 \times 4}{\pi \times 147} \] \[ x^3 = \frac{3696}{460.8} \approx 8 \] Thus, \( x = 2 \).

Step 2: Curved surface area of the cylinder. The formula for the curved surface area (CSA) of the cylinder is: \[ \text{CSA} = 2\pi r h \] Substitute \( r = \frac{7x}{2} \) and \( h = 3x \) with \( x = 2 \): \[ \text{CSA} = 2\pi \times \frac{7 \times 2}{2} \times 3 \times 2 \] \[ \text{CSA} = 2\pi \times 7 \times 6 = 84\pi \] \[ \text{CSA} \approx 264 \, \text{m}^2 \] Final Answer: The correct answer is (b) 264 m\(^2\).