Answer :
The volume of the scoop of ice cream is 14.137 cm³. The height of the cone must be 2.12 cm to fit all the ice cream without spilling if it melts.
Given that,The radius of the ice cream scoop = r1 = 1.5 cm
Radius of the cone = r2 = 1.5 cm.
The scoop of ice cream is in the shape of a whole sphere. Therefore,Volume of the sphere,
V1 = (4/3)πr1³
Volume of the scoop of ice cream = V1
= (4/3)π(1.5)³ cm³
= 14.137 cm³
The scoop of ice cream is sitting in a right cone.
Therefore,Volume of the cone,V2 = (1/3)πr2²h, where h is the height of the cone.We can also find the height of the cone using Pythagoras theorem.
h² = r2² + r1²h = √(r2² + r1²)
h = √(1.5² + 1.5²)
h = √(4.5)h = 2.12 cm
The height of the cone is 2.12 cm.
Therefore,Volume of the cone,
V2 = (1/3)πr2²h
V2 = (1/3)π(1.5)²(2.12) cm³
= 4.71 cm³
Total volume required to fit all the ice cream
= V1 + V2
= 14.137 + 4.71
= 18.847 cm³
Therefore, the volume of the scoop of ice cream is 14.137 cm³. The height of the cone must be 2.12 cm to fit all the ice cream without spilling if it melts.
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