CASE STUDY
An ice-cream seller used to sell different kinds and different shapes of ice-cream like rectangular shaped, conical shape with one end hemispherical, Rectangular shape with one end hemispherical and rectangular brick, etc. One day a child came to his shop and purchased an ice-cream which has the following shape: ice-cream cone as the union of a right circular cone and a hemisphere that has the same (circular) base as the cone. The height of the cone is 9 cm and the radius of its base is 2.5 cm.
Answers
Given :- ice-cream cone as the union of a right circular cone and a hemisphere that has the same (circular) base as the cone. The height of the cone is 9 cm and the radius of its base is 2.5 cm.
To Find :- Volume of ice - cream ?
Solution :-
we know that,
- Volume of cone = (1/3)πr²h
- Volume of hemisphere = (2/3)πr³ .
so,
→ Volume of ice - cream = Volume of cone + Volume of hemisphere
→ Volume of ice - cream = (1/3)πr²h + (2/3)πr³
→ Volume of ice - cream = (1/3)πr²[h + 2r]
since base is same both have same radius as 2.5 cm .
→ Volume of ice - cream = (1/3) * (22/7) * (2.5)² * [9 + 2.5 * 2]
→ Volume of ice - cream = (22/3*7) * 6.25 * 14
→ Volume of ice - cream = (22 * 6.25 * 2)/3
→ Volume of ice - cream = 275/3
→ Volume of ice - cream = 91.67 cm³ (Ans.)
Hence, the volume of the ice cream is 91.67cm³ .
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