Question

Find the lateral area and the surface area of the right cone. Round your answer to the nearest hundredth

Answer 1

The lateral area of a cone is the area of the lateral surface, except the base.

The surface area of a cone is the area of all its surface, which is the lateral side PLUS the base.

The lateral area is given by the formula >>>

`LA=\pi rl`

The surface area is given by the formula >>>

`SA=\pi r^2+\pi rl`

Given

r = 10 cm

h = 24 cm

Let's find l,

`\begin{gathered} r^2+h^2=l^2 \\ 10^2+24^2=l^2 \\ l=\sqrt[]{10^2+24^2} \\ l=26 \end{gathered}`

Let's find the lateral area and the surface area >>>

Lateral Area =

`\begin{gathered} LA=\pi rl \\ LA=\pi(10)(26) \\ LA=260\pi \\ LA=816.81\text{ sq. cm.} \end{gathered}`

Surface Area =

`\begin{gathered} SA=\pi r^2+\pi rl \\ SA=\pi(10)^2+260\pi \\ SA=100\pi+260\pi \\ SA=360\pi \\ SA=1130.97\text{ sq. cm.} \end{gathered}`