There are a cylinder and a cone with height, ^@h^@ and radius ^@r^@. There is also a sphere of the same radius. The height, ^@h^@ of the cylinder and the cone is ^@ 3 ^@ times the radius, ^@r^@. If ^@V_1^@ is the volume of the cylinder, ^@V_2^@ is the volume of the cone and ^@V_3^@ is the volume of the sphere, write the given volumes in ascending order.


Answer:

^@ V_2 < V_3 < V_1 ^@

Step by Step Explanation:
  1. Three solid figures have been provided. The volume of all three solid figures is to be compared.
    h r
    Cylinder
    h r
    Cone

    Sphere
  2. 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 ^@
  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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