Question

a right cone has a radius of 12 cm and a slant height of 28 cm. find the lateral area and surface area of the pyramid. round to three decimal places

Answer 1

Given:

Radius of cone, r = 12 cm

Slant height, L = 28 cm

Let's find the lateral area and surface area of the cone.

Lateral area:

To find the lateral area of the cone, apply the formula:

`A=\pi rl`

Thus, we have:

`\begin{gathered} A=\pi\ast12\ast28 \\ \\ A=\pi\ast336 \\ \\ \text{ A = }1055.575cm^2 \end{gathered}`

Solving further:

Therefore, the lateral area is 1055.575 square centimeters.

Surface Area:

To find the surface area, apply the formula

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

We have:

`SA=(\pi\ast12\ast28)+(\pi\ast12^2)`

Solving further:

`\begin{gathered} SA=(1055.575)+(452.389) \\ \\ \text{ SA=1507.964 cm}^2 \end{gathered}`

Therefore, the surface area is 1507.964 square centimeters.

ANSWER:

Lateral area = 1055.575 cm²

Surafce area = 1507.964 cm²