Question

What is the surface area of the right cone below? 15 O A. 248 units 2 B. 496 units2 C. 184 units2 D. 304units2

Answer 1

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

`A\text{ = pi x r (r + (}\sqrt[]{h^2+r^2)}`

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

`\begin{gathered} \sqrt[]{h^2}\text{ = }\sqrt[]{161} \\ h\text{ = 12.68} \end{gathered}`

Since, h = 12.68

`\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}`

The answer is OPTION C

The answer is 184 pi unit^2