Question

If the curved surface area of a cylinder is 1760 cm\(^2\) and its radius is 14 cm, then its height is:

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

Hint:

The curved surface area of a cylinder is given by \( \text{CSA} = 2 \pi r h \), where \( r \) is the radius and \( h \) is the height.

Answer 1

The Correct Option is B

The formula for the curved surface area (CSA) of a cylinder is: \[ \text{CSA} = 2 \pi r h, \] where \( r \) is the radius and \( h \) is the height. We are given that: \[ \text{CSA} = 1760 \, \text{cm}^2, \quad r = 14 \, \text{cm}. \] Substitute these values into the formula: \[ 1760 = 2 \pi \times 14 \times h. \] Simplify the equation: \[ 1760 = 28 \pi h. \] Now, solve for \( h \): \[ h = \frac{1760}{28 \pi} = \frac{1760}{28 \times 3.14} = \frac{1760}{87.92} \approx 20 \, \text{cm}. \] Thus, the correct answer is 15 cm.