Question

find the lateral surface area and surface area of a cone with a base diameter of 10 m and a slant height of 11 m. write the exact lateral surface area and surface area in terms of π, and be sure to include the correct unit in your answers. (a) lateral surface area: (b) surface area:

Explanation:

Step1: Find the radius of the base

The diameter $d = 10$ m, so the radius $r=\frac{d}{2}=\frac{10}{2}=5$ m.

Step2: Calculate the lateral - surface area

The formula for the lateral - surface area of a cone is $A_{l}=\pi rl$, where $r$ is the radius and $l$ is the slant height. Substitute $r = 5$ m and $l = 11$ m into the formula: $A_{l}=\pi\times5\times11 = 55\pi$ $m^{2}$.

Step3: Calculate the base area

The formula for the area of the base of a cone (a circle) is $A_{b}=\pi r^{2}$. Substitute $r = 5$ m into the formula: $A_{b}=\pi\times5^{2}=25\pi$ $m^{2}$.

Step4: Calculate the surface area

The formula for the surface area of a cone is $A = A_{l}+A_{b}$. Substitute $A_{l}=55\pi$ $m^{2}$ and $A_{b}=25\pi$ $m^{2}$ into the formula: $A=55\pi + 25\pi=80\pi$ $m^{2}$.

Answer:

(a) $55\pi$ $m^{2}$
(b) $80\pi$ $m^{2}$