Answer: 184 pi unit^2
From the figure, we are given a length and a radius
Length = 15
Radius = 8
The surface area of a cone is given as
[tex]A\text{ = pi x r (r + (}\sqrt[]{h^2+r^2)}[/tex]Firstly, we need to find the height of the cone using pythagora's theorem
Hypotenus^2 = opposite^2 + adjacent^2
Hypotenus = 15
Adjacent = 8
H = ?
15^2 = h^2 + 8^2
225 = h^2 + 64
Make h^2 the subject of the formula
h^2 = 225 - 64
h^2 = 161
Take the squareroot of both sides
[tex]\begin{gathered} \sqrt[]{h^2}\text{ = }\sqrt[]{161} \\ h\text{ = 12.68} \end{gathered}[/tex]Since, h = 12.68
[tex]\begin{gathered} A\text{ = pi x 8(8 + (}\sqrt[]{12.68^2+8^2} \\ A\text{ = }\pi\text{x 8 ( 8 + (}\sqrt[]{161\text{ + 64)}} \\ A\text{ = }\pi\text{x 8 ( 8 + }\sqrt[]{225)} \\ A\text{ = pi x 8 ( 8 + 15)} \\ A\text{ = }\pi\text{ x 8 x 23} \\ A=184piunit^2 \end{gathered}[/tex]The answer is OPTION C
The answer is 184 pi unit^2
