The base diameter of a cylinder is 21 cm and the height is 28 cm, the…

The correct answer is Option (2) → (A), (C) and (D) only

To determine which statements are correct, we calculate the properties of a cylinder with base diameter $21\text{ cm}$ and height $28\text{ cm}$.

1. Radius (A)

The radius ($r$) is half of the diameter ($d$):

$r = \frac{d}{2} = \frac{21}{2} = \mathbf{10.5\text{ cm}}$

Statement (A) is correct.

2. Volume (B)

The formula for volume ($V$) is $\pi r^2 h$. Using $\pi = \frac{22}{7}$:

$V = \frac{22}{7} \times (10.5)^2 \times 28$

$V = \frac{22}{7} \times 110.25 \times 28$

$V = 22 \times 110.25 \times 4 = \mathbf{9702\text{ cm}^3}$

Statement (B) is incorrect (given as $12936\text{ cm}^3$).

3. Curved Surface Area (C)

The formula for Curved Surface Area ($CSA$) is $2\pi rh$:

$CSA = 2 \times \frac{22}{7} \times 10.5 \times 28$

$CSA = 44 \times 1.5 \times 28$

$CSA = 66 \times 28 = \mathbf{1848\text{ cm}^2}$

Statement (C) is correct.

4. Total Surface Area (D)

The Total Surface Area ($TSA$) is the sum of the $CSA$ and the area of the two circular bases ($2\pi r^2$):

$\text{Area of 2 bases} = 2 \times \frac{22}{7} \times (10.5)^2 = 2 \times 346.5 = 693\text{ cm}^2$

$TSA = 1848 + 693 = \mathbf{2541\text{ cm}^2}$

Statement (D) is correct.

Conclusion: Statements (A), (C), and (D) are correct.