2012
16. 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.
Answers
Given data :
- 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.
- The height of the conical portion is 4 times the radius of its base.
To find : The radius of the ice cream cone.
Solution : According to given,
→ radius of cylindrical container, r = 6 cm
→ height of cylindrical container, h = 15 cm
Now, we use formula to find volume of cylindrical container.
→ volume of cylindrical container
= π * r² * h
→ volume of cylindrical container
= π * ( 6 )² * 15
→ volume of cylindrical container
= π * 36 * 15
→ volume of cylindrical container
= π * 540 cm³ i.e.
→ volume of cylindrical container
= 540 * π cm³
According to given, the whole ice cream has to be distributed to 10 children in equal cones with hemispherical tops.
→ volume of cone with hemispherical top
= { 540 * π /10 } cm³
→ volume of cone with hemispherical top
= 54 * π cm³
According to given, the height of the conical portion is 4 times the radius of its base.
Now, let radius of cone is r
→ Height of cone, h = 4 * r .....( 1 )
Now, here
→ volume of cone = 1/3 * π * r² * h
{ from ( 1 ) }
→ volume of cone = 1/3 * π * r² * (4 * r )
→ volume of cone = 1/3 * π * 4 * r³
Now,
→ volume of hemispherical top = 2/3 * π * r³
Now, to find the radius of the ice cream cone.
→ volume of cone + volume of hemispherical top = volume of cone with hemispherical top
→ 1/3 * π * 4 * r³ + 2/3 * π * r³ = 54 * π
→ 4/3 * π * r³ + 2/3 * π * r³ = 54 * π
→ ( 4/3 + 2/3 ) * π * r³ = 54 * π
→ 6/3 * π * r³ = 54 * π
→ 2 * π * r³ = 54 * π
{ divide by π both side, we get }
→ 2 r³ = 54
→ r³ = 54/2
→ r³ = 27
→ r = ³√27
→ r = 3 cm
Hence, the radius of the ice cream cone is 3 cm.
Answer:
Radius of ice cream is 3cm
Step-by-step explanation:
My answer was deleted by an user- Shírley
