Question

The areas of the bases of a cone and a cylinder are equal and their curved surface areas are also equal. If the height of the cylinder is \(2\) metre, then the slant height of the cone is:

• A. \(2\) metre
• B. \(3\) metre
• C. \(4\) metre
• D. \(5\) metre

Hint:

Equal base areas \(\Rightarrow\) equal radii. If CSA\(_\text{cyl}\) \(=2\pi rh\) equals CSA\(_\text{cone}\) \(=\pi r\ell\), then \(\ell=2h\) immediately.

Answer 1

The Correct Option is C

Step 1: Use “equal base areas.”
If base areas are equal, their radii are equal. Let the common radius be \(r\).
Step 2: Use “equal curved surface areas.”
Cylinder CSA \(=2\pi r h\).
Cone CSA \(=\pi r \ell\) (where \(\ell\) is the slant height).
Given they are equal: \(2\pi r h=\pi r \ell \Rightarrow \ell=2h.\)
Step 3: Substitute the cylinder’s height.
\(h=2\) m \(\Rightarrow \ell=2\times 2=4\) m.