Question

A cone has a circular base, a perpendicular height of 21cm and a semi vertical angle of 300. Calculate the slant height of the cone. Find the area of its base (Take π = 22/7)

Answer 1

`4158\text{cm}^2`

Explanation:

GIVEN: A cone has a circular base, a perpendicular height of
`21\text{ cm}` and a semi vertical angle of
`300`.

TO FIND: Calculate the slant height of the cone. Find the area of its base.

SOLUTION:

Consider the figure attached.

Let the radius of cone be
`\text{r}`

`tan(\theta)=\frac{\text{perpendicular}}{\text{height}}`

`tan(60)=\frac{\text{radius}}{\text{height}}`

`√(3)=\frac{\text{r}}{\text{21}}`

`\text{r}=21√(3)`

Now,

area of base
`=\pi\text{r}^2=\pi*(21√(3))^2`

`=4158\text{cm}^2`

Hence Area of base of cone is
`4158\text{cm}^2`