Question

The ratio to the total surface area to the lateral surface area of a cylinder whose radius is 20cm and height is 60 cm is

Answer 1

total surface area is 2πrh+2πrr and lateral is 2πrh
and is 4/3

Answer 2

Answer:

Using the formula:

Total surface area of cylinder(S) is given by:

$S = 2\pi r(h+r)$

Lateral surface area of cylinder(L) is given by:

$L = 2\pi rh$

where r is the radius and h is the height of the cylinder respectively.

We have to find the ratio to the total surface area to the lateral surface area of a cylinder.

Given:

radius(r) = 20 cm

height(h) = 60 cm

Ratio of total surface area to lateral surface area of cylinder is:

$\frac{\text{Total surface area of cylinder}}{\text{Lateral surface area of cylinder}}$

then;

$\frac{2\pi r(h+r)}{2 \pi rh}= \frac{h+r}{h}$

Substitute the value we have;

⇒$\frac{60+20}{60}=\frac{80}{60}=\frac{4}{3}$

⇒Ratio of total surface area to lateral surface area of cylinder is 4 : 3

therefore, the ratio to the total surface area to the lateral surface area of a cylinder whose radius is 20 cm and height is 60 cm is 4: 3