A right cylindrical container is filled with ice-cream, whose diameter is 12 cm and height is 15 cm. the whole ice-cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream.
Answers
Answer:
The Diameter of the ice cream is 6 cm.
Step-by-step explanation:
SOLUTION :
Diameter of a cylindrical container = 12 cm
Radius of a cylindrical container, R = 12/2= 6 cm
Height of a cylindrical container, H = 15 cm
Volume of cylindrical container filled with ice cream = πR²H
= π x 6² x 15
= π (36 × 15 )
= 540π cm³
Volume of cylindrical container filled with ice cream = 540π cm³
Amount of ice-cream each child gets = 540π /10 = 54π cm³
Let radius of cone and radius of hemisphere = r cm
Height of cone,h = twice the diameter of the cone
h = 2 ×d = 2 × 2r = 4r
Height of cone ,h = 4r
Volume of the ice cream cone = Volume of hemisphere + volume of cone
54π = 2/3 x π x r³ + 1/3 x π x r² x h
54π = 2/3 x π x r³ + 1/3 x π x r² (4r)
54π = 2/3 x π x r³ + 4/3 x π x r³
54π = 2/3 π x r³ (1 + 2)
54π = 2/3 π x r³ × 3
54π = 2π x r³
54 = 2r³
r³ = 54/2 = 27
r³ = 27
r³ = 3³
r = 3
Radius of the ice cream = 3 cm
Diameter of the ice cream = 2 × r = 2 × 3 = 6 cm
Hence, the Diameter of the ice cream is 6 cm.
HOPE THIS ANSWER WILL HELP YOU….
Answer:
Volume of cylindrical container=πR
2
H=π×6
2
×15=540π㎤
Let radius of base of conical portion be 'r', then diameter=2r
and height=2×2r=4r
10×volume of each cone=volume of container
⇒10[
3
1
πr
2
h+
3
2
πr
3
]=540π⇒10×
3
1
π[r
2
×4r+2r
3
]=540π
⇒6r
3
=162⇒r
3
=27⇒r=
3
27
=3cm
∴Diameter =2r=2×3=6cm