1 Answer

Foo Bar User · Answer 1 · 2024-01-01T03:12:49+0000

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 =

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

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