Alice has two flying disks. One is 12 cm in diameter and the other is 24 cm in diameter. What is the difference between the areas of the two flying disks?

Respuesta :

Answer:

432π cm² or 1356.48 cm²

Step-by-step explanation:

The area of a circle is πr²

The area of the disks are 144π and 576π.

576π-144π = 432π

432π ≈ 1356.48 cm²

The difference between the areas of the two flying disks is

108π cm²

The formula for calculating the area of the disk is expressed as:

[tex]A=\frac{\pi d^2}{4}[/tex]

d is the diameter of the circle

For the disk with a diameter of 12cm

[tex]A_1=\frac{\pi (12)^2}{4}\\A_1=36 \pi[/tex]

For the disk with a diameter of 24cm

[tex]A_2=\frac{\pi (24)^2}{4}\\A_2=144 \pi cm^2[/tex]

The difference in their area is expressed as:

[tex]D = A_2-A_1\\D = 144 \pi - 36 \pi\\D = 108 \pi cm^2[/tex]

Hence the difference between the areas of the two flying disks is

108π cm²

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