Question

The curved surface area of a right circular cone of height 12 cm and base diameter 10 cm is:

• A. 65 π cm²
• B. 75 π cm²
• C. 130 π cm²
• D. 100 π cm²

Answer 1

The Correct Option is A

To find the curved surface area of a right circular cone, we first need to identify the values of the necessary dimensions. Given:

• Height (h) = 12 cm
• Base diameter = 10 cm, thus the radius (r) = 5 cm

The formula for the curved surface area of a cone is:

CSA = πrl

where l is the slant height of the cone. We can calculate l using the Pythagorean theorem:

\(l = \sqrt{h^2 + r^2}\)

Substituting the given values:

\(l = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \, \text{cm}\)

Now substitute r and l into the curved surface area formula:

\(CSA = π \times 5 \times 13 = 65π \, \text{cm}^2\)

Therefore, the curved surface area of the cone is 65π cm².