a small cone with radius of base 3cm is cut from the upper portion of a cone whose radius of the circular base is 12cm and height 2cm . find the Lsa of frustum of the cone
Answers
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
.
Answer:
Answer
Volume of a cone of radius r and height h is =
3
πr
2
h
⇒
3
1
πr
2
h=
125
1
3
1
πR
2
(20)
⇒r
2
h=R
2
125
(20)
−(1)
Also BE∣∣CD (given)
In △ABE & △ACD
∠BAE=∠CAD (common )
∠ABE=∠ACD (corresponding angles)
△ABE∼△ACD by AA criterion
thereby the sides will be in proportion
⇒
CD
BE
=
AC
AB
⇒
R
r
=
20
h
−(3)
Substituting (2) in (1) we get
(
R
2
r
2
)h=20
⇒(
20
h
)
2
h=
125
20
⇒h
3
=
5×5×5
20×20×20
⇒h=
5
20
=4cm
Therefore, the section is made (20−4)cm=16cm above the base of original cone.