A right circular cylinder and aright circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8 : 5, determine the ratio of the radius of the base to the height of either of them.
Answers
Answer:
The ratio of the radius of the base to the height is 3 : 4.
Step-by-step explanation:
SOLUTION :
Given :
Radius of cone = Radius of cylinder = r
Height of cone = Height of cylinder = h
CSA of cylinder : CSA of cone = 8 : 5
2πrh / πrl = 8/5
2h/l = 8/5
h/l = 8/(5×2) = ⅘
5h = 4l
5h = 4(√r² + h²)
[Slant height of a cone,l = √r² + h²]
On squaring both sides,
(5h)² = [4(√r² + h²)]²
25h² = 16(r² + h²)
25h² = 16r² + 16h²
25h² - 16h² = 16r²
9h² = 16r²
r²/h² = 9/16
r/h = √9/16
r/h = ¾
r : h = 3 : 4
Hence, ratio of the radius of the base to the height is 3 : 4.
HOPE THIS ANSWER WILL HELP YOU….
Answer:
Let the radius and height of cylinder and cone be r and h
Let slant height of cone be l
Curved surface area of cylinder=2πrh
Curved surface area of cone=πrl
Ratio=
CSA of cone
CSA of cylinder
=
πrl
2πrh
=
5
8
l
h
=
5
4
Squaring both side
l
2
h
2
=
25
16
l
2
=(
16
25
)h
2
h
2
+r
2
=(
16
25
)h
2
r
2
=(
16
9
)h
2
(
h
r
)
2
=(
4
3
)
2
h
r
=
4
3
Hence ratio of radius to height is 3:4.