Final answer:
The difference in area between the two discs is 108π cm², and when using the approximate value of π, it is 339.1 cm² rounded to the nearest tenth.
Step-by-step explanation:
To find the difference in the areas of two discs, we first calculate the area of each disc individually using the formula A = πr², where 'A' is the area and 'r' is the radius of the disc.
For the disc with a 12 cm diameter, the radius is 6 cm. For the disc with a 24 cm diameter, the radius is 12 cm.
Now let's calculate the area of each disc:
Area of the first disc (12 cm diameter):
A1 = π(6 cm)²
= 36π cm²
Area of the second disc (24 cm diameter):
A2 = π(12 cm)²
= 144π cm²
The difference in area between the two discs is A2 - A1
= 144π cm² - 36π cm²
= 108π cm².
In terms of a numerical value, using π ≈ 3.14, the difference is:
108π cm² ≈ 108(3.14) cm² ≈ 339.1 cm², rounded to the nearest tenth.