Question

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)​

Answer 1

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