Answer:
[tex]4158\text{cm}^2[/tex]
Step-by-step explanation:
GIVEN: A cone has a circular base, a perpendicular height of [tex]21\text{ cm}[/tex] and a semi vertical angle of [tex]300[/tex].
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 [tex]\text{r}[/tex]
[tex]tan(\theta)=\frac{\text{perpendicular}}{\text{height}}[/tex]
[tex]tan(60)=\frac{\text{radius}}{\text{height}}[/tex]
[tex]\sqrt{3}=\frac{\text{r}}{\text{21}}[/tex]
[tex]\text{r}=21\sqrt{3}[/tex]
Now,
area of base [tex]=\pi\text{r}^2=\pi\times(21\sqrt{3})^2[/tex]
[tex]=4158\text{cm}^2[/tex]
Hence Area of base of cone is [tex]4158\text{cm}^2[/tex]
