Question

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 cm\(^3\)
(C) Curved Surface Area = 1848 cm\(^2\)
(D) Total surface area = 2541 cm\(^2\)
Which of the following is/ are correct?
Choose the correct answer from the options given below:

• A. (A), (B) and (D) only
• B. (A), (C) and (D) only
• C. (B), (C) and (D) only
• D. (A), (B) and (C) only

Hint:

When a question asks to verify multiple calculations, do them one by one carefully. It's often helpful to reuse previous results, for instance, TSA = CSA + 2 * (Area of base), to save time.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question requires calculating the radius, volume, curved surface area (CSA), and total surface area (TSA) of a cylinder and verifying the given statements.
Step 2: Key Formula or Approach:
Given: Diameter (d) = 21 cm, Height (h) = 28 cm.
Radius (r) = d/2
Volume (V) = \( \pi r^2 h \)
Curved Surface Area (CSA) = \( 2 \pi r h \)
Total Surface Area (TSA) = \( 2 \pi r (h + r) \)
Use \( \pi = \frac{22}{7} \).
Step 3: Detailed Explanation:
(A) Radius of cylinder:
Radius r = \( \frac{\text{Diameter}}{2} = \frac{21}{2} = 10.5 \) cm. Statement (A) is correct.
(B) Volume:
V = \( \pi r^2 h = \frac{22}{7} \times (10.5)^2 \times 28 \)
V = \( \frac{22}{7} \times (\frac{21}{2})^2 \times 28 = \frac{22}{7} \times \frac{441}{4} \times 28 \)
Simplify by cancelling terms: \( (\frac{28}{7 \times 4}) = 1 \).
V = \( 22 \times 441 = 9702 \) cm\(^3\).
The statement says Volume = 12936 cm\(^3\). Thus, statement (B) is incorrect.
(C) Curved Surface Area:
CSA = \( 2 \pi r h = 2 \times \frac{22}{7} \times 10.5 \times 28 \)
CSA = \( 2 \times \frac{22}{7} \times \frac{21}{2} \times 28 \)
Simplify: \( \frac{2 \times 21}{7 \times 2} = 3 \).
CSA = \( 22 \times 3 \times 28 = 66 \times 28 = 1848 \) cm\(^2\).
Statement (C) is correct.
(D) Total surface area:
TSA = \( 2 \pi r (h + r) \) = CSA + 2(\( \pi r^2 \))
TSA = \( 1848 + 2 \left( \frac{22}{7} \times (10.5)^2 \right) \)
TSA = \( 1848 + 2 \left( \frac{22}{7} \times \frac{441}{4} \right) = 1848 + 2(346.5) \)
TSA = \( 1848 + 693 = 2541 \) cm\(^2\).
Statement (D) is correct.
The correct statements are (A), (C), and (D).
Step 4: Final Answer:
The correct option is (2) which includes statements (A), (C), and (D) only.