A908 m²
B1512 m²
C1848 m²
D1232 m²
Answer:
C. 1848 m²
Read Explanation:
1. Given Information
Ratio of radius ($r$) to height ($h$): $2 : 1$
Let $r = 2x$ and $h = x$Curved Surface Area (CSA): $616\text{ m}^2$
2. Find the Value of $x$
The formula for the curved surface area of a cylinder is:
$\text{CSA} = 2\pi rh$
Substitute the given values ($\pi \approx \frac{22}{7}$):
$616 = 2 \times \frac{22}{7} \times (2x) \times (x)$
$616 = \frac{88}{7}x^2$
Rearranging to solve for $x^2$:
$x^2 = \frac{616 \times 7}{88}$
$x^2 = 7 \times 7 = 49$
$x = 7\text{ m}$
3. Find Radius ($r$) and Height ($h$)
Radius ($r$): $2x = 2 \times 7 = 14\text{ m}$
Height ($h$): $x = 7\text{ m}$
4. Calculate Total Surface Area (TSA)
Method A: Direct Formula
$\text{TSA} = 2\pi r(r + h)$
$\text{TSA} = 2 \times \frac{22}{7} \times 14 \times (14 + 7)$
$\text{TSA} = 2 \times 22 \times 2 \times 21$
$\text{TSA} = 88 \times 21 = \mathbf{1848\text{ m}^2}$
Method B: Shortcut Ratio Method
$\frac{\text{TSA}}{\text{CSA}} = \frac{2\pi r(r + h)}{2\pi rh} = \frac{r + h}{h}$
Substitute the ratios directly ($r=2$, $h=1$):
$\frac{\text{TSA}}{616} = \frac{2 + 1}{1} = \frac{3}{1}$
$\text{TSA} = 616 \times 3 = \mathbf{1848\text{ m}^2}$
Final Answer
The total surface area of the cylinder is $1848\text{ m}^2$.