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

(A) Radius of cylinder = 10.5 cm

(B) Volume = 12936 cm³

(C) Curved surface Area = 1848 cm²

(D) Total surface area = 2541 cm²

Which of the following is/ are correct?

Choose the correct answer from the options given below:

The correct answer is (A), (C) and (D) only.

Let us analyze each statement step-by-step based on the given dimensions of the cylinder:
Given:
Base diameter of the cylinder = 21 cm
Height ($h$) of the cylinder = 28 cm

Step 1: Check Statement (A) - Radius of the cylinder
The radius ($r$) of a cylinder is half of its diameter:

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

Hence, Statement (A) is correct.

Step 2: Check Statement (B) - Volume of the cylinder
The formula for the volume ($V$) of a cylinder is:

$$V=\pi r^{2}h$$

Using $\pi \approx \frac{22}{7}$, $r=10.5\text{cm}$, and $h=28\text{cm}$:

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

$$V=22\times 110.25\times 4$$

$$V=9702{\text{cm}}^3$$

Since the calculated volume is 9702 cm³, Statement (B) is incorrect.

Step 3: Check Statement (C) - Curved Surface Area (CSA) of the cylinder
The formula for the curved surface area of a cylinder is:

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

Substituting the values:

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

$$\text{CSA}=2\times 22\times 1.5\times 28$$

$$\text{CSA}=1848{\text{cm}}^2$$

Hence, Statement (C) is correct.

Step 4: Check Statement (D) - Total Surface Area (TSA) of the cylinder
The total surface area includes the curved surface area and the areas of the two circular bases:

$$\text{TSA}=\text{CSA}+2\pi r^2$$

Substituting the values:

$$\text{TSA}=1848+2\times \frac{22}{7}\times {(10.5)}^2$$

$$\text{TSA}=1848+2\times 22\times 1.5\times 10.5$$

$$\text{TSA}=1848+693$$

$$\text{TSA}=2541{\text{cm}}^2$$

Hence, Statement (D) is correct.

Conclusion:
Statements (A), (C), and (D) are correct, which matches the option (A), (C) and (D) only.