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.
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Let the length of each edge of the cube be a units. ∴ Volume of cube = a3 cube units Since the cylinder is within the cube and it touches all the vertical faces of cube. ∴ Radius of base of the cylinder and the cone = (a/2) units Height of the cylinder and the cone = a units Volume of cylinder = πr2h = π(a/2)2 x a = (22/7) x (a2/4) x a = (11/14)a3 Volume of cone = (1/3) πr2h = (1/3) x π(a/2)2 x a = (22/21) x (a2/4) x a = (11/42)a3 Consider, volume of cube : volume of cylinder : volume of cone = a3 : (11/14)a3 : (11/42)a3 = 1 : (11/14) : (11/42) = 42 : 33 : 11
Let the length of each edge of the cube be a units. ∴ Volume of cube = a3 cube units Since the cylinder is within the cube and it touches all the vertical faces of cube. ∴ Radius of base of the cylinder and the cone = (a/2) units Height of the cylinder and the cone = a units Volume of cylinder = πr2h = π(a/2)2 x a = (22/7) x (a2/4) x a = (11/14)a3 Volume of cone = (1/3) πr2h = (1/3) x π(a/2)2 x a = (22/21) x (a2/4) x a = (11/42)a3 Consider, volume of cube : volume of cylinder : volume of cone = a3 : (11/14)a3 : (11/42)a3 = 1 : (11/14) : (11/42) = 42 : 33 : 11☑️☑️☑️☑️☑️☑️☑️☑️☑️☑️☑️☑️
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Step-by-step explanation:
Assume that the length of all edges of the cube=x units
Formula for volume of cube=x³ cube unit
Due an occurrence that the cylinder is within the cube &it touches all the vertices faces of the cube.
Therefore radius of the base of the cylinder & cone & height of cylinder of a cone=x
Volume of the cylinder=π×{x/2}²×x=22/7×x³/4
11/14x³ cube unit
Volume of cone should be=1/3π{x/2)²×x=11/42 cubic unit
Required ratio=volume of cube:volume of cylinder:volume of cone
=x³:11/14x³:11/42x³=42:33:11
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