The circumference of the base of a cylinder is 30-8 cm. Ite curved surface ared of 289.52cm find the height of the cylinder.
Answers
Answer:
Given :
Circumference of the base of Cylinder is 30.8 cm .
Curved Surface Area is 289.52 cm² .
To Find :
Height of Cylinder .
Solution :
Firstly we will find Radius :
Using Formula :
\longmapsto\tt\boxed{Circumference\:of\:Circle=2\pi{r}}⟼
CircumferenceofCircle=2πr
Putting Values :
\longmapsto\tt{\dfrac{308}{10}=2\times\dfrac{22}{7}\times{r}}⟼
10
308
=2×
7
22
×r
\longmapsto\tt{308\times{7}=44\times{10}\times{r}}⟼308×7=44×10×r
\longmapsto\tt{2156=440r}⟼2156=440r
\longmapsto\tt{r=\cancel\dfrac{2156}{440}}⟼r=
440
2156
\longmapsto\tt\bf{r=4.9\:cm}⟼r=4.9cm
Now ,
\longmapsto\tt{Radius=4.9\:cm}⟼Radius=4.9cm
Using Formula :
\longmapsto\tt\boxed{C.S.A\:of\:Cylinder=2\pi{rh}}⟼
C.S.AofCylinder=2πrh
Putting Values :
\longmapsto\tt{\dfrac{28952}{100}=2\times\dfrac{22}{{\cancel{7}}}\times\dfrac{{\cancel{49}}}{10}\times{h}}⟼
100
28952
=2×
7
22
×
10
49
×h
\longmapsto\tt{\dfrac{28952}{100}=\dfrac{44\times{7}\times{h}}{10}}⟼
100
28952
=
10
44×7×h
\longmapsto\tt{\dfrac{28952}{100}=\dfrac{308\:h}{10}}⟼
100
28952
=
10
308h
\longmapsto\tt{h=\dfrac{{\cancel{28952}}\times{1{\not{0}}}}{{\cancel{308}}\times{10{\not{0}}}}}⟼h=
308
×10
0
28952
×1
0
\longmapsto\tt{h=\dfrac{94}{10}}⟼h=
10
94
\longmapsto\tt\bf{h=9.4\:cm}⟼h=9.4cm
So , The Height of Cylinder is 9.4 cm ...