Question

77. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 4 cm and the diameter of the base is 8 cm. Determine the volume of the toy. If a cube circumscribes the toy, then find the difference of the volumes of cube and the toy. Also, find the total surface
area of the toy.​

Answer 1

Answer:

Volume of toy = Vol. of cone + Vol.of hemisphere

=

3

1

πr

2

H+

3

2

πr

3

=

3

1

πr

2

[H+2r]h

=

3

1

×

7

22

×2×2[2+2×2]

=

3

1

×

7

22

×4×6

2

=25.12cm

3

Volume of cylinder =πr

2

h=

7

22

×2×2[2+2]=

7

22

×16=50.24cm

3

Difference in volume =50.24−25.12=25.12cm

3

Hence, cylinder cover 25.12cm

3

more space.