Question

question 24 of 25
a right cone has a slant height of 6 and a radius of 4. what is its surface area?
a. 16π units²
b. 24π units²
c. 40π units²
d. 56π units²

Explanation:

Step1: Recall the formula for the surface area of a cone

The surface area formula of a cone is \(S=\pi r(r + l)\), where \(r\) is the radius and \(l\) is the slant height.

Step2: Substitute the given values into the formula

Given \(r = 4\) and \(l=6\). Substitute these values into the formula: \(S=\pi\times4\times(4 + 6)\).

Step3: Simplify the expression

First, calculate the value inside the parentheses: \(4+6 = 10\). Then, multiply: \(S=\pi\times4\times10=40\pi\).

Answer:

C. \(40\pi\) units\(^{2}\)