Question

What is the surface area of this cone round to the nearest hundreth

Answer 1

Given:

Diameter of cone = 4 mm

Slant height (l) = 7 mm

Find-: Surface area of the cone.

Sol:

The surface area of a cone is:

`A=\pi r(r+√(r^2+h^2))`

Where,

`\begin{gathered} r(\text{ radius\rparen}=\frac{\text{ Diameter}}{2} \\ \\ h=\text{ Height} \end{gathered}`

Height of cone:

`\begin{gathered} l^2=r^2+h^2 \\ \\ h^2=l^2-r^2 \\ \\ h^2=7^2-2^2 \\ \\ h^2=49-4 \\ \\ h=√(45) \end{gathered}`

So, the surface area of a cone is:

`\begin{gathered} A=\pi r(r+√(r^2+h^2)) \\ \\ A=\pi(2)(2+√(2^2+45)) \\ \\ A=2\pi(2+√(49)) \\ \\ A=2\pi(9) \\ \\ A=18\pi \\ \\ A=18*3.14 \\ \\ A=56.52 \end{gathered}`

So, the surface area of a cone is 56.52