Question

what is the formula for the surface area of a right cone if l = m?
○ sa = πrm + πr²
○ sa = 2πrh
○ sa = πrm
○ sa = 4πr²
○ sa = 2πrh + 2πr²

Explanation:

Step1: Recall Cone Surface Area Formula

The surface area (SA) of a right cone is the sum of the lateral (curved) surface area and the base area. The lateral surface area of a cone is \( \pi r l \) (where \( l \) is the slant height), and the base area is \( \pi r^2 \) (since the base is a circle with radius \( r \)). So the general formula is \( SA = \pi r l + \pi r^2 \).

Step2: Substitute \( l = m \)

Given that \( l = m \), we substitute \( l \) with \( m \) in the formula. So the formula becomes \( SA = \pi r m + \pi r^2 \).

Step3: Eliminate Other Options

• \( SA = 2\pi r h \) is the lateral surface area of a cylinder, not a cone. Eliminate.
• \( SA = \pi r m \) only considers the lateral surface area, not the base. Eliminate.
• \( SA = 4\pi r^2 \) is the surface area of a sphere, not a cone. Eliminate.
• \( SA = 2\pi r h + 2\pi r^2 \) is the surface area of a cylinder, not a cone. Eliminate.

Answer:

A. \( SA = \pi r m + \pi r^2 \)