Question

A cylinder is within the cube touching all the vertical faces. A cone is inside the cylinder. If their heights are same with the same base, find the ratio of their volumes.​

Answer 1

Answer:

42:33:11

Step-by-step explanation:

Given:-

A cylinder is within the cube touching all the vertical faces. A cone is inside the cylinder. If their heights are same with the same base

To Find:-

Ratio of their volume

Solution:-

$\rm \: Let \: edge \: of \: cube \: be \: a \: units. \\ \\ \pink{\boxed{ \red { \sf \: Volume \: of \: cube = (side) ^{3}}}} \\ \\ \rm \: V_{1} =Volume \: of \: cube = {a}^{3}$

Since a cylinder is within the cube and it touches all the vertical faces of the cube.

$\rm \: r = Radius \: of \: cylinder = \frac{a}{2} \\ \rm \: Height \: of \: cylinder = a \\ \\ \red{ \boxed{ \pink{ \sf \: Volume \: of \: cylinder = \pi {r}^{2} h}}} \\ \\ \rm \:V_{2} = Volume \: of \: cylinder \\ \rightarrowtail \rm V_2 = \frac{22}{7} \times \frac{ {a}^{2} }{4} \times a \: cubic \: units \\ \rightarrowtail \rm V_2 = \frac{11}{4} {a}^{3} cubic \: units$

A cone is drawn inside the cylinder such that it has the same base and same height.

$\color{olive} \boxed{ \color{aqua}{ \sf \: Volume \: of \: cone = \frac{1}{3}\pi {r}^{2} h}} \\ \rm V _3 = \frac{1}{3} \times \frac{22}{7} \times \bigg( \frac{ {a}}{2} \bigg) ^{2} \times a \: cubic \: units \\ \longrightarrow \: \rm \: V_3 = \frac{11}{42} {a}^{3} \: cubic \: units \\ \\ \color{navy} \rm \: V_1 : V_2 : V_3 = {a}^{3} : \frac{11}{14} {a}^{3} : \frac{11}{42} {a}^{3} \\ \boxed{\color{olive} \hookrightarrow \:42:33:11}$

Answer 2

Answer:

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Step-by-step explanation:

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