Two similiar cones have volumes 121 cu. units and 96t cu units. If
the curved surface area of the smaller cone is 1571 sq. units, what is
the curved surface area of the larger one?
Answers
Answer:
Let R = radius of base and L = lateral height, H = height of cone. curved surface or lateral surface = A = π R L , and volume = V = π/3* R² H, Similar cones have the same (cone) angle at the apex. Hence the same ratios among R, H and L.
Step-by-step explanation:
Step-by-step explanation:
Small cone volume ⇒
3
1
πr
1
2
h
1
=12π
Large cone volume ⇒
3
1
πr
2
2
h
2
=96π
[Similar cones
r
2
r
1
=
h
2
h
1
]
3
1
πr
2
2
h
2
3
1
πr
1
2
h
1
=
96π
12π
r
2
2
r
1
2
=
8
1
×
h
1
h
2
[
h
1
h
2
=
r
2
r
2
]
r
2
2
r
1
2
=
8
1
×
r
1
r
2
⇒r
1
3
=8r
2
3
⇒r
1
=2r
2
Given surface area of smaller cone ⇒πr
1
r
1
2
+h
2
+πr
1
2
=15π
Large cone =πr
2
2
+πr
2
r
2
2
+h
2
2
=π(2r
1
)
2
+π(2r
1
)
(2r
1
)
2
+(2h
1
)
2
⇒4πr
1
2
+π2r
1
×2
r
1
2
+h
1
2
⇒4(πr
1
2
+πr
1
r
1
2
+h
1
2
)=4×15π
⇒60π.