Question

if the volume of a right circular cone of height 12cm is 68πcm³ . find the diameter of its base.​

Answer 1

Answer:

$\sqrt{68} cm$

Step-by-step explanation:

We know that Volume of a cone = $\frac{1}{3}$π$r^{2}h$

It is given that $h = 12cm$

                       Volume = $68$π$cm^{3}$

⇒ $\frac{1}{3}$π$r^{2}(12)$ = $68$π$cm^{3}$

⇒ $4r^{2} = 68$

⇒ $r^{2} = \frac{68}{4}$

⇒ $r = \sqrt{ \frac{68}{4}}$

⇒ $r =$ ±$\frac{\sqrt{68} }{2}$

We know that radius cannot be negative

⇒ $r =$ $\frac{\sqrt{68} }{2} cm$

We know that diameter = twice the radius

⇒ $D = \frac{\sqrt{68} }{2}*2 = \sqrt{68}cm$