Question

A toy is made by placing a cylinder of radius 7 cm and height 7.7 cm on top of a cube of side 14 cm. What will be the height of the toy?

Answer 1

Given: toy in form of a cone mounted on a hemisphere

radius of hemisphere =3.5 cm

Total height of toy =15.5 cm

To find: Total surface area TSA = ? Volume, V = ?

Solution :

h=12 cm

r=3.5 cm

Assuming that the cone is completed mounted on hemisphere

TSA of toy = CSA of cone + CSA of hemisphere

=πrl+2πr

2

[r→ radius of both cone and hemisphere as it is here]

=πr[l+2r]

=

7

22

×

10

35

[

(12)

2

+(3.5)

2

+2×

10

35

]

=11[

144+12.25

+7]=11[

156.25

+7]

=11(12.5+7)

=11×19.5

=214.5cm

2

Volume of toy =

3

1

πr

2

h+

3

2

πr

3

=

3

1

πr

2

[h+2r]

=

3

1

×

7

22

×

10

35

×

10

25

[12+2×

10

35

]

=

6

77

[12+7]=

6

77×19

=

6

1463

=243.83cm

3

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