A right circular cone has an altitude of $40cm$ and a diameter of $60cm.$ The slant height of the cone is

The correct option is B: $50cm$

Diameter $=60cm$

Radius, $\left(r\right)=\frac{30}{2}=30cm$

Altitude $=$ Height, $\left(h\right)=40cm$

Let the slant height be $Lcm.$

Slant height is given by the formula

$L^2=r^2+h^2$

$\Rightarrow L=\sqrt{r^2+h^2}$

$\Rightarrow L=\sqrt{{30}^2+{40}^2}$

$\Rightarrow L=\sqrt{900+1600}$

$\Rightarrow L=\sqrt{2500}$

$\Rightarrow L=\sqrt{50\times 50}$

$\therefore L=50cm$

Hence, the slant height of the cone is $50cm$