Question

I-10 is being designed in the shape of a cone with a slant height of 18.5 feet and a diameter of 20 ft approximately how much material is needed to cover the lateral area of the tent without any overlap

Answer 1

Solution

Step 1

The lateral area of any shape is the area of the shape without its base area

The expression for the area of a cone is

$\begin{gathered} \text{TSA of a cone = lateral area + }are\text{a of circular base} \\ TSA=\text{ }\pi\times r\times l\text{ +}\pi\times r^2 \end{gathered}$$\begin{gathered} \text{The material n}eeded\text{ to cover the lateral area of the tent is given as} \\ \pi\times r\times l \\ \text{where} \\ \pi=\text{ 3.14} \\ \text{slant height(l) = }18.5ft \\ \text{diameter =}20\operatorname{cm} \\ \text{radius = }\frac{20}{2}=\text{ 10cm},\text{ After substitution} \\ \text{The lateral surface area = 3.1}4\text{ }\times10\times18.5=580.9cm^2 \end{gathered}$

The answer is 580.9 square cm