Question

A right circular cylinder has base radius \(14 \text{ cm}\) and height \(21 \text{ cm}\) then its volume is _____ \(\text{cm}^3\).

• A. 12986
• B. 13986
• C. 13936
• D. 12936

Hint:

Whenever the dimensions are multiples of 7, using \[ \pi = \frac{22}{7} \] makes cancellation much easier and calculations become faster.

Answer 1

The Correct Option is D

Concept: A right circular cylinder is a three-dimensional solid having:
• two parallel circular bases,
• a curved surface joining the bases,
• equal radius throughout the solid. The volume of a cylinder represents the amount of space occupied inside it. The formula for the volume of a cylinder is: \[ V = \pi r^2 h \] where:
• \(r\) = radius of the circular base
• \(h\) = height of the cylinder
• \(\pi \approx \frac{22}{7}\)

Step 1: Write the given measurements carefully. Radius: \[ r = 14 \text{ cm} \] Height: \[ h = 21 \text{ cm} \]

Step 2: Substitute the values into the volume formula. \[ V = \pi r^2 h \] Substituting: \[ V = \frac{22}{7} \times (14)^2 \times 21 \]

Step 3: Calculate the square of the radius. \[ 14^2 = 14 \times 14 = 196 \] Therefore: \[ V = \frac{22}{7} \times 196 \times 21 \]

Step 4: Simplify the expression step-by-step. Since: \[ 196 \div 7 = 28 \] we get: \[ V = 22 \times 28 \times 21 \]

Step 5: Multiply sequentially. First multiply: \[ 28 \times 21 \] \[ 28 \times 21 = 588 \] Now: \[ V = 22 \times 588 \]

Step 6: Final multiplication. \[ 588 \times 22 = 588 \times (20 + 2) \] \[ = 11760 + 1176 \] \[ = 12936 \] Thus: \[ V = 12936 \text{ cm}^3 \]

Step 7: Verify the unit. Since: \[ \text{Volume} = \text{length} \times \text{breadth} \times \text{height} \] the unit becomes: \[ \text{cm}^3 \] which is correct. Final Answer: \[ \boxed{12936 \text{ cm}^3} \]