Respuesta :

Answer:

4 : 9

Step-by-step explanation:

given two similar cylinders with heights in the ratio a : b

Then the ratio of their lateral surface areas is a² : b²

give the heights are 1.2 : 1 .8 = 12 : 18 = 2 : 3 , then

ratio of their lateral areas = 2² : 3² = 4 : 9

msm555

Answer:

4:9

Step-by-step explanation:

The lateral area of a cylinder can be calculated using the formula:

[tex]\Large\boxed{\boxed{\sf \textsf{Lateral Area} = 2 \pi r h}} [/tex]

where

  • [tex]\sf r [/tex] is the radius and
  • [tex]\sf h [/tex] is the height of the cylinder.

Given that the cylinders are similar, their lateral areas will be proportional to the square of their heights.

Let's denote:

  • [tex]\sf h_1 [/tex] as the height of the first cylinder,
  • [tex]\sf h_2 [/tex] as the height of the second cylinder,
  • [tex]\sf A_1 [/tex] as the lateral area of the first cylinder, and
  • [tex]\sf A_2 [/tex] as the lateral area of the second cylinder.

Then, the ratio of their lateral areas is:

[tex]\sf \dfrac{A_1}{A_2} = \left( \dfrac{h_1}{h_2} \right)^2 [/tex]

Given:

  • [tex]\sf h_1 = 1.2 [/tex]
  • [tex]\sf h_2 = 1.8 [/tex]

Substituting these values into the formula, we get:

[tex]\sf \dfrac{A_1}{A_2} = \left( \dfrac{1.2}{1.8} \right)^2 [/tex]

[tex]\sf = \left( \dfrac{2}{3} \right)^2 [/tex]

[tex]\sf = \dfrac{4}{9} [/tex]

So, the ratio of the lateral areas of the two similar cylinders is 4:9.

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