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A container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity is
- a)5390.60 cm3
- b)5100 cm3
- c)5400 cm3
- d)5425.92 cm3
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A container is in the form of a hemispherical bowl mounted by a hollow...
To find the capacity of the container, we need to calculate the volume of the hemispherical bowl and the volume of the cylinder separately, and then add them together.
Given:
Diameter of the sphere = 24 cm
Total height of the container = 16 cm
**Calculating the Volume of the Hemispherical Bowl:**
The radius of the sphere (r) can be calculated by dividing the diameter by 2.
r = 24 cm / 2 = 12 cm
The volume of a hemisphere is given by the formula:
V_hemisphere = (2/3) * π * r^3
Substituting the value of r, we get:
V_hemisphere = (2/3) * π * 12^3
Calculating this value, we find:
V_hemisphere ≈ 3617.92 cm^3
**Calculating the Volume of the Cylinder:**
The height of the cylinder can be calculated by subtracting the radius of the sphere from the total height of the container.
Height of the cylinder = Total height of the container - Radius of the sphere
Height of the cylinder = 16 cm - 12 cm = 4 cm
The radius of the cylinder is the same as the radius of the sphere, which is 12 cm.
The volume of a cylinder is given by the formula:
V_cylinder = π * r^2 * h
Substituting the values of r and h, we get:
V_cylinder = π * 12^2 * 4
Calculating this value, we find:
V_cylinder ≈ 1809.28 cm^3
**Calculating the Total Capacity:**
The total capacity of the container is the sum of the volume of the hemisphere and the volume of the cylinder.
Total capacity = V_hemisphere + V_cylinder
Total capacity ≈ 3617.92 cm^3 + 1809.28 cm^3
Calculating this value, we find:
Total capacity ≈ 5427.20 cm^3
Rounding off to two decimal places, we get:
Total capacity ≈ 5425.92 cm^3
Therefore, the correct answer is option D) 5425.92 cm^3.
Given:
Diameter of the sphere = 24 cm
Total height of the container = 16 cm
**Calculating the Volume of the Hemispherical Bowl:**
The radius of the sphere (r) can be calculated by dividing the diameter by 2.
r = 24 cm / 2 = 12 cm
The volume of a hemisphere is given by the formula:
V_hemisphere = (2/3) * π * r^3
Substituting the value of r, we get:
V_hemisphere = (2/3) * π * 12^3
Calculating this value, we find:
V_hemisphere ≈ 3617.92 cm^3
**Calculating the Volume of the Cylinder:**
The height of the cylinder can be calculated by subtracting the radius of the sphere from the total height of the container.
Height of the cylinder = Total height of the container - Radius of the sphere
Height of the cylinder = 16 cm - 12 cm = 4 cm
The radius of the cylinder is the same as the radius of the sphere, which is 12 cm.
The volume of a cylinder is given by the formula:
V_cylinder = π * r^2 * h
Substituting the values of r and h, we get:
V_cylinder = π * 12^2 * 4
Calculating this value, we find:
V_cylinder ≈ 1809.28 cm^3
**Calculating the Total Capacity:**
The total capacity of the container is the sum of the volume of the hemisphere and the volume of the cylinder.
Total capacity = V_hemisphere + V_cylinder
Total capacity ≈ 3617.92 cm^3 + 1809.28 cm^3
Calculating this value, we find:
Total capacity ≈ 5427.20 cm^3
Rounding off to two decimal places, we get:
Total capacity ≈ 5425.92 cm^3
Therefore, the correct answer is option D) 5425.92 cm^3.
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Community Answer
A container is in the form of a hemispherical bowl mounted by a hollow...
Given that-- the container is in the form of a hemispherical bowl mounted by a hollow cylinder
radius of hemispherical bowl= outer radius of hollow cylinder=24/2=12cm
total height of the container=16cm
height of hollow cylinder=16-( radius of hemispherical bowl)
=16-12=4cm
capacity= volume of hemispherical bowl+ volume of hollow cylinder
=2/3πr³+πr²h
=2/3(3.14) (12) ³+(3.14) (12) ²(4)
=5425.92cm³
hence, option D is correct
radius of hemispherical bowl= outer radius of hollow cylinder=24/2=12cm
total height of the container=16cm
height of hollow cylinder=16-( radius of hemispherical bowl)
=16-12=4cm
capacity= volume of hemispherical bowl+ volume of hollow cylinder
=2/3πr³+πr²h
=2/3(3.14) (12) ³+(3.14) (12) ²(4)
=5425.92cm³
hence, option D is correct
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A container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity isa)5390.60 cm3b)5100 cm3c)5400 cm3d)5425.92 cm3Correct answer is option 'D'. Can you explain this answer?
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A container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity isa)5390.60 cm3b)5100 cm3c)5400 cm3d)5425.92 cm3Correct answer is option 'D'. 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 container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity isa)5390.60 cm3b)5100 cm3c)5400 cm3d)5425.92 cm3Correct answer is option 'D'. 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 container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity isa)5390.60 cm3b)5100 cm3c)5400 cm3d)5425.92 cm3Correct answer is option 'D'. Can you explain this answer?.
A container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity isa)5390.60 cm3b)5100 cm3c)5400 cm3d)5425.92 cm3Correct answer is option 'D'. 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 container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity isa)5390.60 cm3b)5100 cm3c)5400 cm3d)5425.92 cm3Correct answer is option 'D'. 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 container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity isa)5390.60 cm3b)5100 cm3c)5400 cm3d)5425.92 cm3Correct answer is option 'D'. Can you explain this answer?.
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