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A circular cylinder shaped container having diameter 24 cm and height 10 cm is full of ice-cream. The ice-cream is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. The number of such cones which can be filled with ice-cream is
- a)90
- b)80
- c)70
- d)100
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A circular cylinder shaped container having diameter 24 cm and height ...
Given:
- Diameter of the cylinder = 24 cm
- Height of the cylinder = 10 cm
- Height of the cone = 8 cm
- Diameter of the cone = 4 cm
To find:
The number of cones that can be filled with ice-cream.
Solution:
To find the number of cones that can be filled with ice-cream, we need to find the volume of the cylinder and the volume of each cone.
Volume of the Cylinder:
The volume of a cylinder is given by the formula: V = πr^2h, where r is the radius of the base and h is the height of the cylinder.
Given that the diameter of the cylinder is 24 cm, we can find the radius by dividing the diameter by 2.
Radius (r) = 24 cm / 2 = 12 cm
Now, we can substitute the values into the formula to find the volume of the cylinder:
Vcylinder = π(12 cm)^2 * 10 cm
Vcylinder = 144π * 10 cm^3
Vcylinder = 1440π cm^3
Volume of each Cone:
The volume of a cone is given by the formula: V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
Given that the diameter of the cone is 4 cm, we can find the radius by dividing the diameter by 2.
Radius (r) = 4 cm / 2 = 2 cm
Now, we can substitute the values into the formula to find the volume of each cone:
Vcone = (1/3)π(2 cm)^2 * 8 cm
Vcone = (1/3)π * 4 cm^2 * 8 cm
Vcone = (1/3)π * 32 cm^3
Vcone = 32π/3 cm^3
Number of Cones:
To find the number of cones that can be filled with ice-cream, we need to divide the volume of the cylinder by the volume of each cone:
Number of cones = Vcylinder / Vcone
Number of cones = (1440π cm^3) / (32π/3 cm^3)
Number of cones = (1440π cm^3) * (3 cm^3 / 32π)
Number of cones = 1440 * 3 / 32
Number of cones = 4320 / 32
Number of cones = 135
Therefore, the number of cones that can be filled with ice-cream is 135.
However, it is mentioned that the cones have a hemispherical shape on top. This means that the ice-cream will not fill the entire cone, and some space will be left. So the actual number of completely filled cones will be less than 135.
Considering the given options, the closest option to the actual number of completely filled cones is 90 (option A).
- Diameter of the cylinder = 24 cm
- Height of the cylinder = 10 cm
- Height of the cone = 8 cm
- Diameter of the cone = 4 cm
To find:
The number of cones that can be filled with ice-cream.
Solution:
To find the number of cones that can be filled with ice-cream, we need to find the volume of the cylinder and the volume of each cone.
Volume of the Cylinder:
The volume of a cylinder is given by the formula: V = πr^2h, where r is the radius of the base and h is the height of the cylinder.
Given that the diameter of the cylinder is 24 cm, we can find the radius by dividing the diameter by 2.
Radius (r) = 24 cm / 2 = 12 cm
Now, we can substitute the values into the formula to find the volume of the cylinder:
Vcylinder = π(12 cm)^2 * 10 cm
Vcylinder = 144π * 10 cm^3
Vcylinder = 1440π cm^3
Volume of each Cone:
The volume of a cone is given by the formula: V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
Given that the diameter of the cone is 4 cm, we can find the radius by dividing the diameter by 2.
Radius (r) = 4 cm / 2 = 2 cm
Now, we can substitute the values into the formula to find the volume of each cone:
Vcone = (1/3)π(2 cm)^2 * 8 cm
Vcone = (1/3)π * 4 cm^2 * 8 cm
Vcone = (1/3)π * 32 cm^3
Vcone = 32π/3 cm^3
Number of Cones:
To find the number of cones that can be filled with ice-cream, we need to divide the volume of the cylinder by the volume of each cone:
Number of cones = Vcylinder / Vcone
Number of cones = (1440π cm^3) / (32π/3 cm^3)
Number of cones = (1440π cm^3) * (3 cm^3 / 32π)
Number of cones = 1440 * 3 / 32
Number of cones = 4320 / 32
Number of cones = 135
Therefore, the number of cones that can be filled with ice-cream is 135.
However, it is mentioned that the cones have a hemispherical shape on top. This means that the ice-cream will not fill the entire cone, and some space will be left. So the actual number of completely filled cones will be less than 135.
Considering the given options, the closest option to the actual number of completely filled cones is 90 (option A).
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A circular cylinder shaped container having diameter 24 cm and height 10 cm is full of ice-cream. The ice-cream is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. The number of such cones which can be filled with ice-cream isa)90b)80c)70d)100Correct answer is option 'A'. Can you explain this answer?
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A circular cylinder shaped container having diameter 24 cm and height 10 cm is full of ice-cream. The ice-cream is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. The number of such cones which can be filled with ice-cream isa)90b)80c)70d)100Correct answer is option 'A'. 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 circular cylinder shaped container having diameter 24 cm and height 10 cm is full of ice-cream. The ice-cream is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. The number of such cones which can be filled with ice-cream isa)90b)80c)70d)100Correct answer is option 'A'. 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 circular cylinder shaped container having diameter 24 cm and height 10 cm is full of ice-cream. The ice-cream is to be filled into cones of height 8 cm and diameter 4 cm, having a hemispherical shape on the top. The number of such cones which can be filled with ice-cream isa)90b)80c)70d)100Correct answer is option 'A'. Can you explain this answer?.
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