Question

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height ?

• A. 3:7
• B. 7:6
• C. 6:7
• D. 7:3

Answer 1

Answer:

D. 7:3

The ratio of the diameter to the height of the cylindrical pillar is 7 : 3.

Here is the step-by-step derivation:

1. Identify the Formulas

• Curved Surface Area (CSA) of a cylinder = $2\pi rh = 264 \text{ m}^2$

• Volume (V) of a cylinder = $\pi r^2h = 924 \text{ m}^3$

2. Find the Radius ($r$)

Divide the Volume by the Curved Surface Area:
$\frac{\text{Volume}}{\text{CSA}} = \frac{\pi r^2h}{2\pi rh} = \frac{r}{2}$

Now, substitute the given numerical values:
$\frac{r}{2} = \frac{924}{264}$
$\frac{r}{2} = 3.5$
$r = 3.5 \times 2 = \mathbf{7 \text{ m}}$

3. Find the Height ($h$)

Use the CSA formula ($2\pi rh = 264$) to solve for $h$ (taking $\pi = \frac{22}{7}$):
$2 \times \frac{22}{7} \times 7 \times h = 264$
$44 \times h = 264$
$h = \frac{264}{44} = \mathbf{6 \text{ m}}$

4. Find the Ratio of Diameter ($d$) to Height ($h$)

• Diameter ($d$) = $2 \times r = 2 \times 7 = \mathbf{14 \text{ m}}$

• Height ($h$) = $\mathbf{6 \text{ m}}$

$\text{Ratio} = \frac{\text{Diameter}}{\text{Height}} = \frac{14}{6} = \frac{7}{3}$