the radius and height of a cylinder are in the ratio of 4:5 and its volume is 2160m³. Find its diameter and height.
Answers
Step-by-step explanation:
Ratio of Radius and Height of Cylinder is 4:5.
Volume of Cylinder is 2160m³
Find Diameter and Height.
Let the Radius be 4x and Height be 5x.
\boxed{ \bf{Volume \: of \: Cylinder = \pi {r}^{2}h }}
VolumeofCylinder=πr
2
h
\longrightarrow\sf{Volume = \pi {r}^{2}h}⟶Volume=πr
2
h
\longrightarrow\sf{2160 = \dfrac{22}{7} \times {(4x)}^{2} \times 5x}⟶2160=
7
22
×(4x)
2
×5x
\longrightarrow\sf{ \cancel{2160} = \dfrac{22}{7} \times {16x}^{2} \times \cancel{5}x}⟶
2160
=
7
22
×16x
2
×
5
x
\longrightarrow\sf{432= \dfrac{22}{7} \times {16x}^{2} \times x}⟶432=
7
22
×16x
2
×x
\longrightarrow\sf{432 \times 7= 22 \times {16x}^{2} \times x}⟶432×7=22×16x
2
×x
\longrightarrow\sf{3024 = 352 {x}^{3} }⟶3024=352x
3
\longrightarrow \sf{ \cancel\dfrac{3024}{352} = {x}^{3} }⟶
352
3024
=x
3
\longrightarrow \sf{ \dfrac{189}{22} = {x}^{3} }⟶
22
189
=x
3
\longrightarrow \sf{ \sqrt[3]{\dfrac{189}{22}} = x }⟶
3
22
189
=x
\longrightarrow \sf{x = \dfrac{5.73}{2.80} }⟶x=
2.80
5.73
\longrightarrow \large\sf{x = 2.04}⟶x=2.04