Question

10.) Find the surface area of this cone shaped megaphone. Use 3.14 for

pi. (Assume it is a solid)


2.25 ft slant hight
1.2 ft diameter
Image in the solid 6 in by 6 in

Options for answers are

5.3 ft
5.4 ft
53 ft
54ft

Answer 1

5.4 ft²

Explanation:

To find the surface area of the cone-shaped megaphone, use the surface area of a cone formula.

`\boxed{\begin{minipage}{7cm}\underline{Surface area of a cone}\\\\$S.A.=\pi r^2+\pi rl$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius of the circular base.\\ \phantom{ww}$\bullet$ $l$ is the slant height of the cone.\\\end{minipage}}`

The radius of a circle is half its diameter.

Therefore, if the diameter of the cone's circular base is 1.2 ft, then its radius is r = 0.6 ft.

Given values:

• r = 0.6 ft
• l = 2.25 ft
• π ≈ 3.14

Substitute the values into the formula and solve:

`\begin{aligned}\textsf{Surface area}&=3.14 \cdot0.6^2+3.14 \cdot 0.6 \cdot 2.25\\&=3.14 \cdot 0.36+3.14 \cdot 0.6 \cdot 2.25\\&=1.1304+1.884 \cdot 2.25\\&=1.1304+4.239\\&=5.3694\\&=5.4\; \sf ft^2\;(nearest\;tenth)\end{aligned}`

Therefore, the surface area of the cone-shaped megaphone is 5.4 ft² (rounded to the nearest tenth).