Subjects geometry

Circle Area 5Ffbb0

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem:** Find the area of each circle in terms of $\pi$. The formula for the area of a circle is: $$\text{Area} = \pi r^2$$ where $r$ is the radius of the circle. 2. **Important rule:** If the problem gives the diameter $d$, remember that the radius $r$ is half the diameter: $$r = \frac{d}{2}$$ 3. **Calculations:** - Circle 1: radius $r = 16$ ft $$\text{Area} = \pi (16)^2 = 256\pi \text{ ft}^2$$ - Circle 2: radius $r = 12$ in $$\text{Area} = \pi (12)^2 = 144\pi \text{ in}^2$$ - Circle 3: diameter $d = 6$ yd, so radius $r = \frac{6}{2} = 3$ yd $$\text{Area} = \pi (3)^2 = 9\pi \text{ yd}^2$$ - Circle 4: diameter $d = 10$ yd, so radius $r = \frac{10}{2} = 5$ yd $$\text{Area} = \pi (5)^2 = 25\pi \text{ yd}^2$$ - Circle 5: diameter $d = 10$ ft, so radius $r = \frac{10}{2} = 5$ ft $$\text{Area} = \pi (5)^2 = 25\pi \text{ ft}^2$$ - Circle 6: diameter $d = 7$ in, so radius $r = \frac{7}{2} = 3.5$ in $$\text{Area} = \pi (3.5)^2 = 12.25\pi \text{ in}^2$$ 4. **Question 7:** Radius $r = 4$ in $$\text{Area} = \pi (4)^2 = 16\pi \text{ in}^2$$ The correct answer is **c) 16\pi in²**. 5. **Question 8:** Diameter $d = 32$ yd, radius $r = \frac{32}{2} = 16$ yd $$\text{Area} = \pi (16)^2 = 256\pi \text{ yd}^2$$ The correct answer is **d) 256\pi yd²**. 6. **Question 9:** Diameter of pizza $d = 26$ in, radius $r = \frac{26}{2} = 13$ in $$\text{Area} = \pi (13)^2 = 169\pi \text{ in}^2$$ **Final answers:** 1) $256\pi$ ft² 2) $144\pi$ in² 3) $9\pi$ yd² 4) $25\pi$ yd² 5) $25\pi$ ft² 6) $12.25\pi$ in² 7) $16\pi$ in² (option c) 8) $256\pi$ yd² (option d) 9) $169\pi$ in²