A cone of height 12 cm and base radlus 3 cm is cut into two parts by a plane parallel to its base at a helght of 8cm from its vertex. The volume of
the larger part will be:
Options
441/3
32/3
76TT/3
641/3
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Answer:
Given, r
1
=12cm,h
1
=20cm,r
2
=3cm,h
2
=?
We know,
r
2
r
1
=
h
2
h
1
∴
3
12
=
h
2
20
∴h
2
=
12
3×20
=5cm
∴ The cut to be made at 5cm from the vertex.
Volume of the frustum=
3
1
πh(r
1
2
+r
2
2
+r
1
r
2
)
=
3
1
×
7
22
×15(12
2
+3
2
+12×3)=
7
110
×(144+9+36)
=
7
110
×189=2,970
∴Volume of the frustum=2,970cm
3
.
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