Example 7: A solid toy is in the form of a
hemisphere surmounted by a right circular cone. The
height of the cone is 2 cm and the diameter of the
base is 4 cm. Determine the volume of the toy. If a
right circular cylinder circumscribes the toy, find the
difference of the volumes of the cylinder and the toy.
(Take TT= 3.14)
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Volume Of Toy is 16 cm³
Difference between volume of toy and volume of cylinder is 9.12 cm³
Step-by-step explanation:
GIVEN
Height = 2 cm
Diameter = 4 cm
π = 3.14
___________________________
TO FIND
Volume Of Toy
Difference between volume of toy and volume of cylinder
___________________________
VOLUME OF TOY
We know that,
Toy is in the shape of hemisphere
We know that,
Volume Of Hemisphere = ⅔ × π × r³
We know that,
Radius = Diameter / 2
Radius = 4 / 2
Radius = 2
Radius = 2 cm
We know that,
Volume Of Hemisphere = ⅔ × π × r³
Volume Of Hemisphere = ⅔ × 3.14 × 2³
Volume Of Hemisphere = ⅔ × 3.14 × 8
Volume Of Hemisphere = 0.6 × 3.14 × 8
Volume Of Hemisphere = Approximately 16
Volume Of Hemisphere = 16 cm³
Volume Of Toy is 16 cm³
___________________________
Difference
We know that,
Volume Of Cylinder = π × r² × h
Volume Of Cylinder = 3.14 × 2² × 2
Volume Of Cylinder = 3.14 × 4 × 2
Volume Of Cylinder = 25.12
Volume Of Cylinder = 25.12 cm³
Difference = Volume Of Cylinder - Volume Of Toy
Difference = 25.12 - 16
Difference = 9.12
Difference = 9.12 cm³
Difference between volume of toy and volume of cylinder is 9.12 cm³
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