Question

1. find the surface area of a cone with a radius of 45.7 mm and a height of 39.7 mm.

Explanation:

Step1: Calculate the slant height \( l \)

Use the Pythagorean theorem \( l=\sqrt{r^{2}+h^{2}} \). Given \( r = 45.7\) mm and \( h=39.7\) mm.

$$
LATEXBLOCK0
$$

Step2: Calculate the surface area \( S \)

The surface area formula of a cone is \( S=\pi r(r + l)\). Substitute \( r = 45.7\) and \( l\approx60.536\)

$$
LATEXBLOCK1
$$

Answer:

The surface area of the cone is approximately \(15247.8\) \(mm^{2}\)