Question

Find the surface area of a conical hat, if its slant height is three times the radius and the base diameter of a hat is $4$ inches. (Use $\pi =3$).

• A. $48{in}^2$
• B. $36i{n}^2$
• C. $48in$
• D. $46{in}^2$

Answer 1

The correct option is B $36i{n}^2$

We know, the total surface area of a cone is $A=\pi r(r+l)$.

But since it a hat, therefore, we will have to subtract the circular area because the hat is not completely covered with a circular part.

Here, the diameter is $4$ $inch$ and therefore, the radius is half of diameter that is $r=2$ $inch$ and it is also given that slant height is thrice the radius that is $l=(3\times 2)=6$ $inch$. We use $\pi =3$.

Thus,

$\text{Area of hat}=\pi r(r+l)-\pi r^2=3\times 2(2+6)-3\times 2\times 2=3\times 2\times 8-12=36$ in${}^2$.

Hence, the surface area of the conical hat is $36$ in${}^2$.

Therefore, option $B$ is correct.