Question

The circumference of the base of a $9m$ high wooden solid cone is $44m$. The slant height of the cone is:

• A. $\sqrt{110}m$
• B. $\sqrt{130}m$
• C. $\sqrt{150}m$
• D. $\sqrt{180}m$

Answer 1

Answer: (B)

Let $r$ be the radius of the base of cone.

So, circumference of the base of the cone $=44m$.

$\Rightarrow 2\pi r=44m$.

$\Rightarrow 2\times \frac{22}{7}\times r=44$ $[\because \pi =\frac{22}{7}]$

$\Rightarrow r=\frac{44\times 7}{22\times 2}=7m$.

So the radius of the cone $=7m$.

$\therefore$ Slant height $l=\sqrt{r^2+h^2}$

$\Rightarrow l=\sqrt{7^2+9^2}=\sqrt{49+81}=\sqrt{130}m$.

Therefore, option $B$ is correct.