A large circle and a small circle are shown.
The radius of the large circle is 12 cm.
radius of large circle : radius of small circle = 4 : 1
Work out the shaded area. Give your answer in terms of π.

To find the shaded area, we need to calculate the area of the large circle and subtract the area of the small (unshaded) circle. **Step 1: Find the radius of the small circle.** We are given the ratio of the radii: Radius_large : Radius_small = 4 : 1 We know the radius of the large circle is 12 cm. This corresponds to the '4' in the ratio. So, 4 parts = 12 cm. To find the value of 1 part, we divide by 4: 1 part = 12 cm / 4 = 3 cm. The radius of the small circle is 1 part, so Radius_small = 3 cm. **Step 2: Calculate the area of the large circle.** The formula for the area of a circle is A = πr². Area_large = π × (12)² = π × 144 = 144π cm². **Step 3: Calculate the area of the small circle.** Area_small = π × (3)² = π × 9 = 9π cm². **Step 4: Calculate the shaded area.** Shaded Area = Area_large - Area_small Shaded Area = 144π - 9π = 135π cm². The answer is required in terms of π, so this is the final answer.