1. **Find the volume of a cone with height 6 in and radius 1 in** (since diameter is 2 in, radius is half): Formula for the volume of a cone: $$V = \frac{1}{3}\pi r^2 h$$ Calculate radius: $$r = \frac{2}{2} = 1 \text{ in}$$ Calculate volume: $$V = \frac{1}{3} \pi (1)^2 (6) = 2\pi \approx 6.283 \text{ in}^3$$ 2. **Find the volume of a sphere with radius 5.3 in**: Volume formula: $$V = \frac{4}{3}\pi r^3$$ Calculate volume: $$V = \frac{4}{3}\pi (5.3)^3 = \frac{4}{3}\pi (148.877) = 198.503\pi \approx 623.04 \text{ in}^3$$ 3. **Find the volume of a cone with height 2.7 cm and radius 8.3 cm**: Volume formula: $$V = \frac{1}{3} \pi r^2 h$$ Calculate volume: $$V = \frac{1}{3} \pi (8.3)^2 (2.7) = \frac{1}{3} \pi (68.89)(2.7) = \frac{1}{3} \pi (185.998) = 61.999\pi \approx 194.80 \text{ cm}^3$$ 4. **Find the volume of a sphere with radius 9.17 cm**: Volume formula: $$V = \frac{4}{3} \pi r^3$$ Calculate volume: $$V = \frac{4}{3}\pi (9.17)^3 = \frac{4}{3} \pi (770.75) = 1027.66\pi \approx 3226.07 \text{ cm}^3$$ 5. **Tennis balls in a cylinder problem:** a. Given circumference of tennis ball = 8 in, find volume. Find radius from circumference: $$C = 2\pi r \implies r = \frac{C}{2\pi} = \frac{8}{2\pi} = \frac{8}{6.283} \approx 1.273 \text{ in}$$ Volume of one ball (sphere): $$V = \frac{4}{3} \pi (1.273)^3 = \frac{4}{3} \pi (2.061) = 2.748\pi \approx 8.63 \text{ in}^3$$ b. There are 3 tennis balls in the cylinder. Calculate cylinder volume with height 8.25 in and radius 1.43 in: $$V_{cyl} = \pi r^2 h = \pi (1.43)^2 (8.25) = \pi (2.045) (8.25) = 16.87\pi \approx 52.98 \text{ in}^3$$ Calculate total volume of 3 tennis balls: $$3 \times 8.63 = 25.89 \text{ in}^3$$ Calculate remaining space in cylinder: $$V_{remaining} = V_{cyl} - V_{balls} = 52.98 - 25.89 = 27.09 \text{ in}^3$$ **Final answers:** 1) Cone volume = $6.283$ in$^3$ 2) Sphere volume = $623.04$ in$^3$ 3) Cone volume = $194.80$ cm$^3$ 4) Sphere volume = $3226.07$ cm$^3$ 5a) Tennis ball volume = $8.63$ in$^3$ 5b) Space in cylinder not occupied by balls = $27.09$ in$^3$