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A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.
- a)6.4 cm
- b)4.2 cm
- c)2.1 cm
- d)5.6 cm
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A right circular cone is 4.1 cm high and the radius of its base is 2.1...
Volume of cone of r = 2.1 cm &
h. = 4.1cm =
h. = 4.1cm =
Volume of cone of r = 2.1 cm & h = 4.3 cm
= 
Let radius of the sphere be r cm.
Now, Volume of sphere = Sum of Volume of both cones.
Now, Volume of sphere = Sum of Volume of both cones.
∴ Diameter of sphere = 4.2 cm.
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A right circular cone is 4.1 cm high and the radius of its base is 2.1...
Given:
Height of first cone (h1) = 4.1 cm
Radius of base of first cone (r1) = 2.1 cm
Height of second cone (h2) = 4.3 cm
Radius of base of second cone (r2) = 2.1 cm
To find: Diameter of the sphere formed after melting and recasting the cones
1. Volume of the first cone:
The volume of a cone is given by the formula:
V1 = (1/3) * π * r1^2 * h1
Substituting the given values, we get:
V1 = (1/3) * π * (2.1 cm)^2 * 4.1 cm
2. Volume of the second cone:
Similarly, the volume of the second cone is given by:
V2 = (1/3) * π * r2^2 * h2
Substituting the given values, we get:
V2 = (1/3) * π * (2.1 cm)^2 * 4.3 cm
3. Total volume of the two cones:
The total volume of the two cones will be equal to the volume of the sphere formed after melting and recasting.
V_total = V1 + V2
4. Volume of the sphere:
The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * r_sphere^3
5. Equating the volumes:
Setting V_total = V_sphere and rearranging the equation, we get:
(4/3) * π * r_sphere^3 = V1 + V2
6. Substituting the values and solving for r_sphere:
(4/3) * π * r_sphere^3 = (1/3) * π * (2.1 cm)^2 * 4.1 cm + (1/3) * π * (2.1 cm)^2 * 4.3 cm
Simplifying the equation, we get:
(4/3) * π * r_sphere^3 = (1/3) * π * (2.1 cm)^2 * (4.1 cm + 4.3 cm)
Cancelling out the common terms and solving, we get:
r_sphere^3 = (2.1 cm)^2 * (8.4 cm)
Taking the cube root of both sides, we get:
r_sphere = ∛((2.1 cm)^2 * (8.4 cm))
7. Calculating the diameter of the sphere:
The diameter of the sphere is given by:
d_sphere = 2 * r_sphere
Substituting the value of r_sphere, we get:
d_sphere = 2 * ∛((2.1 cm)^2 * (8.4 cm))
Simplifying the expression, we get:
d_sphere = 2 * ∛(8.82 cm^3)
Calculating the cube root, we get:
d_sphere = 2 * 2.1 cm
Finally, evaluating the expression, we get:
d_sphere = 4.2 cm
Therefore, the diameter of the sphere formed after melting and recasting the cones is 4.2 cm. Hence, option B is correct.
Height of first cone (h1) = 4.1 cm
Radius of base of first cone (r1) = 2.1 cm
Height of second cone (h2) = 4.3 cm
Radius of base of second cone (r2) = 2.1 cm
To find: Diameter of the sphere formed after melting and recasting the cones
1. Volume of the first cone:
The volume of a cone is given by the formula:
V1 = (1/3) * π * r1^2 * h1
Substituting the given values, we get:
V1 = (1/3) * π * (2.1 cm)^2 * 4.1 cm
2. Volume of the second cone:
Similarly, the volume of the second cone is given by:
V2 = (1/3) * π * r2^2 * h2
Substituting the given values, we get:
V2 = (1/3) * π * (2.1 cm)^2 * 4.3 cm
3. Total volume of the two cones:
The total volume of the two cones will be equal to the volume of the sphere formed after melting and recasting.
V_total = V1 + V2
4. Volume of the sphere:
The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * r_sphere^3
5. Equating the volumes:
Setting V_total = V_sphere and rearranging the equation, we get:
(4/3) * π * r_sphere^3 = V1 + V2
6. Substituting the values and solving for r_sphere:
(4/3) * π * r_sphere^3 = (1/3) * π * (2.1 cm)^2 * 4.1 cm + (1/3) * π * (2.1 cm)^2 * 4.3 cm
Simplifying the equation, we get:
(4/3) * π * r_sphere^3 = (1/3) * π * (2.1 cm)^2 * (4.1 cm + 4.3 cm)
Cancelling out the common terms and solving, we get:
r_sphere^3 = (2.1 cm)^2 * (8.4 cm)
Taking the cube root of both sides, we get:
r_sphere = ∛((2.1 cm)^2 * (8.4 cm))
7. Calculating the diameter of the sphere:
The diameter of the sphere is given by:
d_sphere = 2 * r_sphere
Substituting the value of r_sphere, we get:
d_sphere = 2 * ∛((2.1 cm)^2 * (8.4 cm))
Simplifying the expression, we get:
d_sphere = 2 * ∛(8.82 cm^3)
Calculating the cube root, we get:
d_sphere = 2 * 2.1 cm
Finally, evaluating the expression, we get:
d_sphere = 4.2 cm
Therefore, the diameter of the sphere formed after melting and recasting the cones is 4.2 cm. Hence, option B is correct.
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A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer?
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A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer?.
A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A right circular cone is 4.1 cm high and the radius of its base is 2.1 cm. Another right circular cone is 4.3 cm high and the radius of the base is 2.1 cm. Both the cones are melted and recast into a sphere. Find the diameter of the sphere.a)6.4 cmb)4.2 cmc)2.1 cmd)5.6 cmCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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