Question

Please help me with this please ASAP ASAP please ASAP

Answer 1

Given:

The diagram of a cone.

To find:

The lateral area, surface area and volume of the cone.

Solution:

From the given diagram, we get

Radius of the cone = 6

Slant height of the cone = 10

Suppose
`h` be the height of the cone.

According to Pythagoras theorem:

`hypotenuse^2=Perpendicular^2+Base^2`

Using the Pythagoras theorem, we get

`10^2=(6)^2+h^2`

`100=36+h^2`

`100-36=h^2`

`64=h^2`

Taking square root on both sides, we get

`√(64)=h`

`8=h`

The lateral area of a cone is:

`A_L=\pi rl`

`A_L=\pi (6)(8)`

`A_L=48\pi`

The surface area of a cone is:

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

`A_S=\pi (6)(8)+\pi (6)^2`

`A_S=48\pi +36\pi`

`A_S=84\pi`

Volume of cone is:

`V=(1)/(3)\pi r^2h`

`V=(1)/(3)\pi (6)^2(8)`

`V=(288)/(3)\pi`

`V=96\pi`

Hence, the lateral area of a cone is
`48\pi` sq. units, the surface area of a cone is
`84\pi` sq. units and the volume of the cone is
`96\pi` cubic units.