Question

The total surface area of a conical jar is $740{ft}^2$. If its slant height is two times the radius, then what is the base diameter of the conical jar? (use $\pi =3$).

• A. $18.12$ ft
• B. $18.10$ ft
• C. $18.24$ ft
• D. $18.31$ ft

Answer 1

The correct option is A $18.12$ ft

We know, the total surface area of cone=$\pi rs+\pi r^2$, where $s$ is the slant height and $r$ is the radius of the base of the cone.

Given, $s=2r$.

Also, the total surface area =$740f{t}^2$.

$\therefore \pi rs+\pi r^2=740$.

Substituting $s=2r$ and $\pi =3$ in the above equation we get,

$3\times r\times 2r+3r^2=740$

$\Rightarrow 3\times 2r^2+3r^2=740$

$\Rightarrow 6r^2+3r^2=740$

$\Rightarrow 9r^2=740$

$\Rightarrow r^2=\frac{740}{9}$

$\Rightarrow r^2=82.22$

$\Rightarrow r=\sqrt{82.22}$

$\Rightarrow r=9.06$.

We know, diameter $d=$ twice of radius.

$\therefore d=2r$

$⟹d=2\times 9.06$

$⟹d=18.12ft$.

Therefore, option $A$ is correct.