Question

1. find the surface area of this cone. (image of a cone with slant height 5 m and radius 4 m) options: 54π m², 36π m², 60π m², 20π m²

Explanation:

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

The surface area \( S \) of a cone is given by the sum of the lateral (curved) surface area and the area of the base. The formula is \( S=\pi rl+\pi r^{2} \), where \( r \) is the radius of the base, and \( l \) is the slant height of the cone.

Step2: Identify the values of \( r \) and \( l \)

From the diagram, the radius \( r = 4\space m \) and the slant height \( l=5\space m \).

Step3: Calculate the lateral surface area

The lateral surface area is \( \pi rl \). Substituting \( r = 4 \) and \( l = 5 \), we get \( \pi\times4\times5=20\pi \).

Step4: Calculate the area of the base

The area of the base (a circle) is \( \pi r^{2} \). Substituting \( r = 4 \), we get \( \pi\times4^{2}=\pi\times16 = 16\pi \).

Step5: Calculate the total surface area

Add the lateral surface area and the base area: \( S=20\pi + 16\pi=36\pi \space m^{2} \).

Answer:

\( 36\pi\space m^{2} \) (corresponding to the option "36π m²")