Question

If the radius of a candle is $r,$ then the ratio of its volume to curved surface area is:

• A. $\frac{r}{4}$
• B. $r$
• C. $\frac{r}{2}$
• D. $\frac{2}{r}$

Answer 1

The correct option is C $\frac{r}{2}$

Given, the radius of the candle is $r.$
Let the height of the candle be $h.$

Step 1: $\text{Volume of the candle = area of the base}\times \text{height}$
$=\pi r^2\times h$
$=\pi r^{2}h$

Step 2: The curved surface of the cylinder is a rectangle. One side length is the height, and the other side length is the circumference of the circle.

$\text{Curved surface area of the candle = circumference of the circle}\times \text{height}$
$=2\pi r\times h$
$=2\pi rh$

Step 3: Ratio of volume to curved surface area
$=\pi r^{2}h:2\pi rh$
Divide both sides by $\pi rh$
$=\frac{\pi r^{2}h}{\pi rh}:\frac{2\pi rh}{\pi rh}$
$=r:2$
$=\frac{r}{2}$

Hence, option (c.) is the correct choice.