Let's solve each problem step by step.
---
Part 1: Find the area of each circle. Leave answers in terms of π.
The formula for the
area of a circle is:
$$
A = \pi r^2
$$
where $ r $ is the radius.
---
####
1)
- Radius $ r = 15 $
- Area:
$$
A = \pi (15)^2 = \pi \cdot 225 = \boxed{225\pi}
$$
---
####
2)
- Diameter = 10 → Radius $ r = \frac{10}{2} = 5 $
- Area:
$$
A = \pi (5)^2 = \pi \cdot 25 = \boxed{25\pi}
$$
---
Part 2: Find the area of each shaded sector. Leave answers in terms of π.
The formula for the
area of a sector is:
$$
A_{\text{sector}} = \frac{\theta}{360^\circ} \cdot \pi r^2
$$
where $ \theta $ is the central angle in degrees.
---
####
3)
- Central angle $ \theta = 40^\circ $
- Radius $ r = 15 $
- Area:
$$
A = \frac{40}{360} \cdot \pi (15)^2 = \frac{1}{9} \cdot \pi \cdot 225 = \frac{225}{9} \pi = \boxed{25\pi}
$$
---
####
4)
- Central angle $ \theta = 40^\circ $
- Radius $ r = 12 $
- Area:
$$
A = \frac{40}{360} \cdot \pi (12)^2 = \frac{1}{9} \cdot \pi \cdot 144 = \frac{144}{9} \pi = \boxed{16\pi}
$$
---
####
5)
- The shaded region is a
quarter circle because there's a right angle (90°) marked.
- So, $ \theta = 90^\circ $
- Radius $ r = 8 $
- Area:
$$
A = \frac{90}{360} \cdot \pi (8)^2 = \frac{1}{4} \cdot \pi \cdot 64 = \frac{64}{4} \pi = \boxed{16\pi}
$$
---
####
6)
- Central angle $ \theta = 36^\circ $
- Radius $ r = 6 $
- Area:
$$
A = \frac{36}{360} \cdot \pi (6)^2 = \frac{1}{10} \cdot \pi \cdot 36 = \frac{36}{10} \pi = \boxed{3.6\pi}
$$
(Or as a fraction: $ \frac{18}{5}\pi $)
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✔ Final Answers:
1) $ \boxed{225\pi} $
2) $ \boxed{25\pi} $
3) $ \boxed{25\pi} $
4) $ \boxed{16\pi} $
5) $ \boxed{16\pi} $
6) $ \boxed{3.6\pi} $ or $ \boxed{\frac{18}{5}\pi} $
Let me know if you'd like explanations with diagrams or visual breakdowns!
Parent Tip: Review the logic above to help your child master the concept of area of sector worksheet.
