If the height of a cylinder is 11 cm and the curved surface area is $968 cm^2$, then the radius of the cylinder will be

Question

Accepted Answer

To determine the radius of the cylinder, we need to use the formula for the curved surface area (CSA) of a cylinder, which is given by:

$$ \text{CSA} = 2\pi rh $$

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

Given:
- Curved Surface Area (CSA) = 968 cm²
- Height (h) = 11 cm

We need to find the radius $ r $.

Substitute the given values into the formula:

$$ 968 = 2\pi r \times 11 $$

Simplify the equation:

$$ 968 = 22\pi r $$

To solve for $ r $, divide both sides by $ 22\pi $:

$$ r = \frac{968}{22\pi} $$

Using the approximation $ \pi \approx 3.14 $:

$$ r = \frac{968}{22 \times 3.14} $$

$$ r = \frac{968}{69.08} $$

$$ r \approx 14.01 $$

Rounding to the nearest whole number, the radius $ r $ is approximately 14 cm.

Therefore, the correct answer is Option 3: 14 cm.

**Explanation for why other options are incorrect:**

1. **Option 1: 10 cm**
   - If the radius were 10 cm, the curved surface area would be calculated as:
     $$ \text{CSA} = 2\pi \times 10 \times 11 = 220\pi \approx 691.6 \, \text{cm}^2 $$
   - This is significantly less than the given 968 cm², so 10 cm cannot be the correct radius.

2. **Option 2: 11 cm**
   - If the radius were 11 cm, the curved surface area would be:
     $$ \text{CSA} = 2\pi \times 11 \times 11 = 242\pi \approx 760.88 \, \text{cm}^2 $$
   - This is also less than 968 cm², so 11 cm is not the correct radius.

3. **Option 4: 8 cm**
   - If the radius were 8 cm, the curved surface area would be:
     $$ \text{CSA} = 2\pi \times 8 \times 11 = 176\pi \approx 552.64 \, \text{cm}^2 $$
   - This is much less than 968 cm², so 8 cm cannot be the correct radius.

Thus, the only option that satisfies the given conditions is Option 3: 14 cm.