40. A toy is in the shape of a cone surrounding a hemisphere. The total height of the toy is 7cm and
the radius of the hemisphere is 3cm. Find the total surface area and volume of the toy
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Step-by-step explanation:
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
solution
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