1. A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the
height of the cone are 6 cm and 4 cm respectively. Find the surface area of the toy?
(Take n = 3.14)
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1
Answer:
r=3cm,h=4cm
l
2
=r
2
+h
2
=3
2
+4
2
=9+16
l
2
=25
l=
25
=5cm
Spherical portion r=3cm
Surface area of the toy= CSA of hemisphere+ CSA of cone
=2πr
2
+πrl=2×
7
22
×3×3cm
2
+
7
22
×3×5cm
2
=
7
396
cm
2
+
7
330
cm
2
=
7
726
cm
2
=103.71cm
2
Surface area of the toy=103.71cm
2
Volume of the toy= Volume of hemisphere+ Volume of cone
=
3
2
πr
3
+
3
1
πr
2
h=
3
2
×
7
22
×3×3×3cm
3
+
3
1
×
7
22
×3×3×4cm
3
=
7
396
cm
3
+
7
264
cm
3
=
7
660
cm
3
∴ Volume of the toy=94.28cm
3
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