Question

If the curved surface area of a cylinder is 1760 cm² and its diameter is 28 cm, then its height is:

• A. 10 cm
• B. 15 cm
• C. 20 cm
• D. 40 cm

Hint:

Use the formula \( A = 2 \pi r h \) for the curved surface area of a cylinder to find the height when the radius and area are known.

Answer 1

The Correct Option is C

The formula for the curved surface area of a cylinder is: \[ A = 2 \pi r h, \] where \( r \) is the radius and \( h \) is the height. We are given that the curved surface area is 1760 cm² and the diameter is 28 cm, so the radius \( r = \frac{28}{2} = 14 \) cm. Substitute the values into the formula: \[ 1760 = 2 \pi (14) h. \] Solving for \( h \): \[ 1760 = 28 \pi h \quad \Rightarrow \quad h = \frac{1760}{28 \pi} \approx \frac{1760}{87.92} \approx 20 \, \text{cm}. \] Thus, the height of the cylinder is \( \boxed{20 \, \text{cm}} \).