There are a cylinder and a cone with height, ^@h^@ and radius ^@ | Math Question and Answer

Answer:

$V_2 < V_3 < V_1$

Step by Step Explanation:

Three solid figures have been provided. The volume of all three solid figures is to be compared.

Cylinder

Cone

Sphere

It is given that the height, $h$ of the cylinder and the cone $= 3 × r$
The volume of the cylinder, $V_1 = \pi r^2 h = \pi r^2 (3 r) = 3 \pi r^3$
The volume of the cone, $V_2 = \dfrac{ 1 }{ 3 } \pi r^2 h = \dfrac{ 1 }{ 3 } \pi r^2 (3 r) = \pi r^3$
The volume of the sphere, $V_3 = \dfrac{ 4 }{ 3 } \pi r^3 = 1.33 \pi r^3$
On comparing the volumes of the three figures, $\begin{align} & \pi r^3 < 1.33 \pi r^3 < 3 \pi r^3 \\ \implies & V_2 < V_3 < V_1 \end{align}$

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