Question

The base radius of a solid right circular cone is equal to the length of the radius of a
solid sphere. If the volume of the sphere is twice of that of the cone, then let us write
by calculating the ratio of the height and base radius of the cone.​

Answer 1

Let, Base radius of a solid right circular cone = Radius of solid sphere = r units

Height of the cone be h units

Given :

Volume of sphere = 2 × ( Volume of cone )

We know that

• Volume of sphere = 4/3 × πr³
• Volume of cone = 1 / 3 × πr²h

⇒ 4/3 × πr³ = 2 × ( 1 / 3 × πr²h )

Cancelling r² one both sides since radius of cone and sphere are equal

⇒ 4/3 × πr = 2 / 3 × πh

Cancelling π and 2/3 on both sides

⇒ 2r = h

⇒ 2 = h / r

⇒ h / r = 2

⇒ h : r = 2 : 1

Therefore the ratio of height and radius of cone is 2 : 1

Answer 2

Answer:

• Radius of Cone & Sphere are Equal.

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$:\implies\textsf{Vol. of Sphere = 2(Vol. of Cone)}\\\\\\:\implies\sf \dfrac{4}{3}\pi r^3=2\bigg(\dfrac{1}{3} \pi r^2h\bigg)\\\\\\:\implies\sf \dfrac{4}{3}\pi r^3 =\dfrac{2}{3} \pi r^2h\\\\\\:\implies\sf \dfrac{\frac{4}{3}\pi r^3}{ \frac{2}{3}\pi r^2} = h\\\\\\:\implies\sf 2r = h\\\\\\:\implies\sf \dfrac{2}{1} = \dfrac{h}{r}\\\\\\:\implies \underline{ \boxed{\sf h:r = 2 :1}}$

⠀

$\therefore\:\underline{\textsf{Ratio of Height \& Base of Cone is \textbf{2 : 1}}}.$