a right circular cylinder is within a cube touching all its vertical sides. a right circular cone is inside the cylinder. if their heights are equal with 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
please make as brainlist
∴ 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
please make as brainlist
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