Question

17. The ratio of the total surface area to the lateral surface area of a cylinder with
base radius 80 cm and height 20 cm is​

Answer 1

Given :

• Radius of Cylinder = 80cm.
• Height of Cylinder = 20cm.

To Find :

• Ratio of the Total Surface Area to the Lateral Surface Area of Cylinder.

Solution :

$\longmapsto\tt{C.S.A\:of\:Cylinder=2\pi{rh}}$

$\longmapsto\tt{T.SA\:of\:Cylinder=2\pi{r(r+h)}}$

Now ,

$\longmapsto\tt{\dfrac{T.S.A}{C.S.A}=\dfrac{{\cancel{2\pi{r}}h}}{{\cancel{2\pi{r}}(r+h)}}}$

$\longmapsto\tt{\dfrac{r+h}{h}}$

$\longmapsto\tt{\dfrac{80+20}{20}}$

$\longmapsto\tt{\cancel\dfrac{100}{20}}$

$\longmapsto\tt{\dfrac{5}{1}}$

$\longmapsto\tt\bold{5:1}$

Therefore , The Ratio of T.S.A to C.S.A of Cylinder is 5:1 ..

Answer 2

Step-by-step explanation:

C.S.AofCylinder=2πrh

\longmapsto\tt{T.SA\:of\:Cylinder=2\pi{r(r+h)}}⟼T.SAofCylinder=2πr(r+h)

Now ,

\longmapsto\tt{\dfrac{T.S.A}{C.S.A}=\dfrac{{\cancel{2\pi{r}}h}}{{\cancel{2\pi{r}}(r+h)}}}⟼

C.S.A

T.S.A

=

2πr

(r+h)

2πr

h

\longmapsto\tt{\dfrac{r+h}{h}}⟼

h

r+h

\longmapsto\tt{\dfrac{80+20}{20}}⟼

20

80+20

\longmapsto\tt{\cancel\dfrac{100}{20}}⟼

20

100

\longmapsto\tt{\dfrac{5}{1}}⟼

1

5

\longmapsto\tt\bold{5:1}⟼5:1

Therefore , The Ratio of T.S.A to C.S.A of Cylinder is 5:1