Question

given a right cone with radius r and slant height s, what does the formula πrs represent?
a. the lateral area
b. the volume
c. the base area
d. the area

Explanation:

The formula for the lateral (or curved) surface area of a right - cone is \(A=\pi rs\), where \(r\) is the radius of the base of the cone and \(s\) is the slant height.

• The volume of a cone is given by \(V = \frac{1}{3}\pi r^{2}h\) (where \(h\) is the height of the cone), so option B is incorrect.
• The base area of a cone (since the base is a circle) is given by \(A_{base}=\pi r^{2}\), so option C is incorrect.
• The total surface area of a cone is \(A_{total}=\pi r(r + s)=\pi r^{2}+\pi rs\) (sum of the base area and the lateral area). Since the given formula is \(\pi rs\) and not \(\pi r(r + s)\), option D (which is too vague as "the area" without specification) is incorrect.

So, the formula \(\pi rs\) represents the lateral area of the right - cone.

Answer:

A. The lateral area