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Answers
Answer:
16) r = 2.6 cm 17) capacity = 3811.5 cm³
Step-by-step explanation:
you can see the pic
Question:
A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is 4 times the radius of its base, find the radius of the ice cream cone.
Answer:
Radius of ice cream cone = 3 cm
Step-by-step explanation:
Given:
Radius of cylindrical container = 6 cm
Height of cylindrical container = 15 cm
Number of children the ice cream is distributed to = 10
Height of the cone = 4 × radius of the base
To Find:
Radius of the ice cream cone
Solution:
Let us first find the volume of the cylindrical container.
Volume of a cylinder = πr²h
where r is the radius and h is the height
Substitute the data,
Volume of cylindrical container = Volume of ice cream = π × 6 × 6 × 15
⇒ 540 π cm³
Now finding the radius of a cone with hemispherical top.
Let radius of the cone be r
Hence by given,
Height = 4 r
Volume of ice cream cone = Volume of cone + Volume of hemisphere
Volume of ice cream cone = 1/3 π × r² × h + 2/3 π r³
where r is the radius and h is the height
Substitute the data,
Volume of ice cream cone = 1/3 × π × r² × 4r + 2/3 × π × r³
= 4/3 π r³ + 2/3 π r³
= 2/3 π r³ (2 + 1)
= 2/3 π r³ × 3
= 2 π r³
Therefore the volume of 10 ice cream cones would be 10 × 2 π r³ = 20 π r³ cm³
By given,
Volume of ice cream in cylindrical container = Volume of ice cream in 10 cones
Substitute the data,
540 π = 20 π r³
540/20 = r³
r = ∛27
r = 3 cm
Hence the radius of the ice cream cone is 3 cm.
Question:
A vessel in the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5 cm. Find its capacity.
Answer:
Capacity of vessel = 3811.5 cm³
Step-by-step explanation:
Given:
Diameter of the hemisphere = 21 cm
Total height of the vessel = 14.5 cm
To Find:
Capacity of the vessel
Solution:
Capacity of the vessel = Volume of hemisphere + Volume of cylinder
Finding the volume of hemisphere,
Volume of hemisphere = 2/3 π r³
Substitute the data,
Volume of hemisphere = 2/3 × 22/7 × (21/2)³
= 9702/4 = 2425.5 cm³
Now finding the volume of cylinder,
Volume of cylinder = π r² h
Here,
Height of the cylinder = Total height of vessel - Radius of the hemisphere
= 14.5 - 21/2
= 4 cm
Diameter of hemisphere = Diameter of cylinder
Substitute the data,
Volume of cylinder = 22/7 × (21/2)² × 4
= 1386 cm³
Therefore total capacity of the vessel is given by,
Capacity of the vessel = 2425.5 cm³ + 1386 cm³
= 3811.5 cm³
Therefore the capacity of the vessel is 3811.5 cm³.