The total surface area of a circular cylinder which has a height of 14 metres and a base of radius 3 metres, is :

Question

Accepted Answer

To determine the total surface area of a circular cylinder, we use the formula:

$$ \text{Total Surface Area} = 2\pi r(h + r) $$

where $ r $ is the radius of the base and $ h $ is the height of the cylinder.

Given:
- Radius ($ r $) = 3 metres
- Height ($ h $) = 14 metres

Substituting these values into the formula:

$$ \text{Total Surface Area} = 2\pi \times 3 \times (14 + 3) $$

$$ = 2\pi \times 3 \times 17 $$

$$ = 6\pi \times 17 $$

$$ = 102\pi $$

Using the approximation $\pi \approx 3.14159$:

$$ 102\pi \approx 102 \times 3.14159 $$

$$ \approx 320.57 \, \text{sq. metre} $$

Thus, the total surface area of the cylinder is approximately 320.57 square metres, which corresponds to Option 3.

**Explanation for why each option is incorrect:**

1. **Option 1: 302.75 sq. metre** - This value is incorrect because it underestimates the total surface area calculated using the formula. The correct calculation yields approximately 320.57 sq. metre, which is higher than 302.75 sq. metre.

2. **Option 2: 203.57 sq. metre** - This value is incorrect as it significantly underestimates the total surface area. The calculation clearly shows that the total surface area is much larger than 203.57 sq. metre.

3. **Option 4: 230.75 sq. metre** - This value is also incorrect because it does not match the calculated total surface area of approximately 320.57 sq. metre. It is an underestimate of the actual surface area.

In conclusion, Option 3 is the correct answer as it accurately reflects the calculated total surface area of the cylinder based on the given dimensions.