Question

find the surface area of this cone. use 3.14 for π. surface area of a cone la = πrl sa = la + b sa = ? m² round your answer to the nearest tenth.

Explanation:

Step1: Calculate the lateral area (LA)

The formula for lateral area of a cone is \(LA=\pi rl\). Here, \(r = 4\) m and \(l=6\) m. Substitute the values:
\(LA = 3.14\times4\times6\)
\(LA=3.14\times24 = 75.36\) \(m^{2}\)

Step2: Calculate the base area (B)

The base of a cone is a circle. The formula for the area of a circle is \(B=\pi r^{2}\). Substitute \(r = 4\) m:
\(B=3.14\times4^{2}=3.14\times16 = 50.24\) \(m^{2}\)

Step3: Calculate the surface area (SA)

The formula for the surface area of a cone is \(SA=LA + B\). Substitute \(LA = 75.36\) \(m^{2}\) and \(B = 50.24\) \(m^{2}\):
\(SA=75.36+50.24=125.6\) \(m^{2}\)

Answer:

\(125.6\) \(m^{2}\)