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The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
- a)9.7 cm3
- b)77.6 cm3
- c)58.2 cm3
- d)19.4 cm3
Correct answer is option 'D'. Can you explain this answer?
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The volume of the largest right circular cone that can be cut out from...
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3.
Edge of the cube = 4.2 cm
i.e 2r = 4.2
r = 4.2/2 = 2.1 cm
h = 4.2 cm
Volume of the cone = 1/3 * pi * r^2 * h
=> 1/3 * 22/7 * 2.1 * 2.1 * 4.2
=> 19.404 cm^3
Hence, the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3.
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The volume of the largest right circular cone that can be cut out from...
Given: Edge of the cube = 4.2 cm
To find: Volume of the largest right circular cone that can be cut out from the cube.
Explanation:
The largest possible right circular cone that can be cut from a cube would have a base equal to one of the faces of the cube and a height equal to the diagonal of the cube. Let's find the diagonal of the cube first.
Diagonal of the cube = √(edge² + edge² + edge²)
= √(4.2² + 4.2² + 4.2²)
= √(17.64 + 17.64 + 17.64)
= √52.92
= 7.28 cm
Now, the radius of the base of the cone would be half of the edge of the cube. Therefore, the radius of the cone = 4.2/2 = 2.1 cm
Using the formula for the volume of a cone, we get:
Volume of the cone = (1/3)πr²h
= (1/3)π(2.1)²(7.28)
= 19.43 cm³
Therefore, the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.4 cm³ (approx).
Hence, option D is the correct answer.
To find: Volume of the largest right circular cone that can be cut out from the cube.
Explanation:
The largest possible right circular cone that can be cut from a cube would have a base equal to one of the faces of the cube and a height equal to the diagonal of the cube. Let's find the diagonal of the cube first.
Diagonal of the cube = √(edge² + edge² + edge²)
= √(4.2² + 4.2² + 4.2²)
= √(17.64 + 17.64 + 17.64)
= √52.92
= 7.28 cm
Now, the radius of the base of the cone would be half of the edge of the cube. Therefore, the radius of the cone = 4.2/2 = 2.1 cm
Using the formula for the volume of a cone, we get:
Volume of the cone = (1/3)πr²h
= (1/3)π(2.1)²(7.28)
= 19.43 cm³
Therefore, the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.4 cm³ (approx).
Hence, option D is the correct answer.
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The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm isa)9.7 cm3b)77.6 cm3c)58.2 cm3d)19.4 cm3Correct answer is option 'D'. Can you explain this answer?
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