A solid toy is in the form of a hemisphere surmounted by a right circular cone. height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find how much more space it will cover.
Answers
Answer:
The remaining volume of the cylinder when toy is inserted into it is 8 π cm³.
Step-by-step explanation:
SOLUTION :
Given :
Radius of the cone, cylinder and hemisphere (r) = 2 cm
Height of the cone (h) = 2 cm
Height of the cylinder (H) = 4 cm
Volume of the cylinder , V1 = πr²H
V1 = π × 2² × 4 cm³ = π × 4 × 4 = 16π
V1 = 16π cm³
Volume of the cone , V2 = 1/3πr²h
V2 = ⅓ × π × 2² × 2
V2 = (π × 4 × 2)/3 = 8π/3
V2 = 8π/3 cm³
Volume of the hemisphere, V3 = ⅔ × πr³
= ⅔ × π × 2³ = ⅔ × π × 8 = 16π/3
V3 = 16π/3 cm³
Remaining volume of the cylinder when the toy is inserted to it, V = volume of the cylinder - (volume of the hemisphere + volume of a cone)
V = V1 - (V2 + V3)
V = 16π - ( 8π/3 + 16π/3)
V = 16π - (24π/3)
V = 16π - 8π
V = 8π cm³
Hence , the remaining volume of the cylinder when toy is inserted into it is 8 π cm³.
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ANSWER:---
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