Question

a cylinder is within the cube touching all the vertical faces a cone is inside the cylinder if there height are the same with the same base find the ratio of their volume

Answer 1

hope it will help you

Answer 2

AnswEr:

Let the length of each edge of the cube be a units. Then,

${V}_{1}$ = Volume of the cube = a³ cubic units.

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

$\therefore \: \tt \: r = radius \: of \: the \: base \: of \: the \: \\ \tt \: cylinder \: = \frac{a}{2} , h \: = height \: of \: the \: \\ \tt \: cylinder \: = a \\ \\ \therefore \: \tt \: v_{2} = volume \: of \: the \: cylinder \: = \pi {r}^{2} h \\ \\ \leadsto \sf \: v_{2} = \frac{22}{7} \times \frac{ {a}^{2} }{4} \times a \: cubic \: units \: \\ \\ \leadsto \sf \: v_{2} \: = \frac{11}{14} {a}^{3} \: cubic \: units \:$

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

$\therefore \tt \: v_{3} = volume \: of \: cone \: = \frac{1}{3} \pi {r}^{2} h \\ \\ \leadsto \sf \: v_{3} = \frac{1}{3} \times \frac{22}{7} \times \frac{ {(a)}^{ 2} }{ {(2)}^{2} } \times a \: cubic \: units \: \\ \\ \leadsto \sf \: v_{3} \: = \frac{11}{42} {a}^{3} \: cubic \: units \:$

${V}_{1}$ : ${V}_{2}$ : ${V}_{3}$ = 42 : 33 : 11