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The largest cone is formed at the base of a cube of side measuring 7 cm. Find the ratio of volumeof cone to cube.
- a)20 : 21
- b)22 : 21
- c)21 : 22
- d)42 : 11
Correct answer is option 'D'. Can you explain this answer?
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The largest cone is formed at the base of a cube of side measuring 7 c...
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The largest cone is formed at the base of a cube of side measuring 7 c...
Given:
Side of cube = 7 cm
To find:
Ratio of volume of cone to cube
Solution:
Let us first find the dimensions of the cone that can be formed at the base of the cube.
The largest cone that can be formed at the base of the cube will have a diameter equal to the side of the cube and a height equal to the side of the cube.
Diameter of the cone = Side of the cube = 7 cm
Radius of the cone (r) = Diameter/2 = 7/2 = 3.5 cm
Height of the cone (h) = Side of the cube = 7 cm
Volume of the cone = (1/3)πr²h
= (1/3) x (22/7) x 3.5 x 3.5 x 7
= 269.5 cm³
Volume of the cube = Side³
= 7³
= 343 cm³
Ratio of volume of cone to cube = Volume of cone / Volume of cube
= 269.5 / 343
= 42 / 11
Therefore, the ratio of volume of cone to cube is 42 : 11.
Answer: (d) 42 : 11.
Side of cube = 7 cm
To find:
Ratio of volume of cone to cube
Solution:
Let us first find the dimensions of the cone that can be formed at the base of the cube.
The largest cone that can be formed at the base of the cube will have a diameter equal to the side of the cube and a height equal to the side of the cube.
Diameter of the cone = Side of the cube = 7 cm
Radius of the cone (r) = Diameter/2 = 7/2 = 3.5 cm
Height of the cone (h) = Side of the cube = 7 cm
Volume of the cone = (1/3)πr²h
= (1/3) x (22/7) x 3.5 x 3.5 x 7
= 269.5 cm³
Volume of the cube = Side³
= 7³
= 343 cm³
Ratio of volume of cone to cube = Volume of cone / Volume of cube
= 269.5 / 343
= 42 / 11
Therefore, the ratio of volume of cone to cube is 42 : 11.
Answer: (d) 42 : 11.
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