Question

Find the ratio of the total surface area to the lateral
surface area of a cylinder whose radius is
80 cm and height 20 cm?​

Answer 1

Given:

• Radius of the cylinder = 80 cm

• Height of the cylinder = 20 cm

To calculate:

• The ratio of the total surface area to the lateral surface area of a cylinder.

Calculation:

As per the given question,

⇒ Ratio = T.S.A of cylinder : L.S.A of cylinder

We can write it as,

$\longrightarrow \sf { Ratio = \dfrac{ {T.S.A}_{(Cylinder)} }{ {L.S.A}_{(Cylinder)} } }$

>> T.S.A of cylinder = 2πr ( r + h )

>> L.S.A of cylinder = 2πrh

$\longrightarrow \sf { Ratio = \dfrac{ \cancel{2\pi r}\: (r+h)}{ \cancel{2 \pi r} \: h} }$

$\longrightarrow \sf { Ratio = \dfrac{ (r+h)}{ h} }$

Substitute the values we are given in the question.

$\longrightarrow \sf { Ratio = \dfrac{ (80 \: cm + 20\: cm)}{ 20 \: cm} }$

$\longrightarrow \sf { Ratio = \dfrac{ 100\: cm}{ 20 \: cm} }$

$\longrightarrow \sf { Ratio = \dfrac{ 10}{ 2 } }$

$\longrightarrow \sf { Ratio = \dfrac{ 5}{ 1 } }$

$\longrightarrow \sf\red { Ratio = 5:1 }$

Therefore, the ratio of the total surface area to the lateral surface area of a cylinder is 5:1.

More formulae:

Formulae related to right circular cylinder:

• T.S.A = 2πr(r+h)

• L.S.A = 2πrh

• Volume = πr²h

Formulae related to hollow cylinder:

• T.S.A = 2π ( R + r )(h + R - r)

• L.S.A = 2π ( R + r )h

• Volume = π (R² - r²) h

[R =External radius, r = internal radius]

Answer 2

Step-by-step explanation:

As per the given question,

⇒ Ratio = T.S.A of cylinder : L.S.A of cylinder

We can write it as,

{ {T.S.A}of {(Cylinder)} }/{ {L.S.A}_{(Cylinder)} } }

>> T.S.A of cylinder = 2πr ( r + h )

>> L.S.A of cylinder = 2πrh

⟶Ratio=( r+h)/h

Substitute the values we are given in the question.

⟶Ratio= 80cm +20 cm /20

Ratio= 1/5

⟶Ratio=5:1

Therefore, the ratio of the total surface area to the lateral surface area of a cylinder is 5:1.

hopefully it will work ☺️☺️