1. **Problem:** Find the volume of a cylinder with diameter 18 cm and height 38 cm. Round to the nearest tenth. 2. **Formula:** Volume of a cylinder is given by $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Step 1:** Find the radius: $$r = \frac{18}{2} = 9\text{ cm}$$ 4. **Step 2:** Substitute values: $$V = \pi \times 9^2 \times 38 = \pi \times 81 \times 38$$ 5. **Step 3:** Calculate volume: $$V = 3078\pi \approx 9667.1\text{ cm}^3$$ --- 1. **Problem:** Find the volume of a tennis ball (sphere) with diameter 2 inches. Round to nearest tenth. 2. **Formula:** Volume of a sphere is $$V = \frac{4}{3} \pi r^3$$ 3. **Step 1:** Radius: $$r = \frac{2}{2} = 1\text{ inch}$$ 4. **Step 2:** Substitute: $$V = \frac{4}{3} \pi (1)^3 = \frac{4}{3} \pi$$ 5. **Step 3:** Calculate: $$V \approx 4.1888\text{ in}^3$$ --- 1. **Problem:** Find volume of grain in a silo (cylinder) with diameter 6 m, height 10 m, half full. 2. **Formula:** $$V = \pi r^2 h$$ 3. **Step 1:** Radius: $$r = \frac{6}{2} = 3\text{ m}$$ 4. **Step 2:** Full volume: $$V = \pi \times 3^2 \times 10 = 90\pi$$ 5. **Step 3:** Half full volume: $$\frac{1}{2} \times 90\pi = 45\pi \approx 141.4\text{ m}^3$$ --- 1. **Problem:** Find radius of sphere with volume 250 cm³. 2. **Formula:** $$V = \frac{4}{3} \pi r^3$$ 3. **Step 1:** Solve for $r$: $$r^3 = \frac{3V}{4\pi} = \frac{3 \times 250}{4\pi} = \frac{750}{4\pi}$$ 4. **Step 2:** Calculate: $$r^3 \approx \frac{750}{12.566} \approx 59.68$$ 5. **Step 3:** Cube root: $$r = \sqrt[3]{59.68} \approx 3.9\text{ cm}$$ --- 1. **Problem:** Find volume of sphere with radius 6.7 m. 2. **Formula:** $$V = \frac{4}{3} \pi r^3$$ 3. **Step 1:** Substitute: $$V = \frac{4}{3} \pi (6.7)^3$$ 4. **Step 2:** Calculate: $$6.7^3 = 300.763$$ 5. **Step 3:** Volume: $$V = \frac{4}{3} \pi \times 300.763 = 1259.3\text{ m}^3$$ --- 1. **Problem:** Find height of cylinder with volume 1472 m³ and radius 14 m. 2. **Formula:** $$V = \pi r^2 h$$ solve for $h$: $$h = \frac{V}{\pi r^2}$$ 3. **Step 1:** Calculate denominator: $$\pi \times 14^2 = \pi \times 196 = 615.75$$ 4. **Step 2:** Calculate height: $$h = \frac{1472}{615.75} \approx 2.39\text{ m}$$ --- 1. **Problem:** Find volume of sphere with diameter 31 m. 2. **Formula:** $$V = \frac{4}{3} \pi r^3$$ 3. **Step 1:** Radius: $$r = \frac{31}{2} = 15.5\text{ m}$$ 4. **Step 2:** Calculate volume: $$V = \frac{4}{3} \pi (15.5)^3 = \frac{4}{3} \pi 3723.875 = 15601.3\text{ m}^3$$ --- 1. **Problem:** Find gallons of water in pool 8 ft across and 3 ft deep. 1 cubic foot = 7.5 gallons. 2. **Formula:** Volume of cylinder: $$V = \pi r^2 h$$ 3. **Step 1:** Radius: $$r = \frac{8}{2} = 4\text{ ft}$$ 4. **Step 2:** Volume: $$V = \pi \times 4^2 \times 3 = 48\pi \approx 150.8\text{ ft}^3$$ 5. **Step 3:** Gallons: $$150.8 \times 7.5 = 1131.0\text{ gallons}$$ --- 1. **Problem:** Find volume of cone with height 23 cm and radius 7 m (convert units to cm: 7 m = 700 cm). 2. **Formula:** $$V = \frac{1}{3} \pi r^2 h$$ 3. **Step 1:** Substitute: $$V = \frac{1}{3} \pi (700)^2 \times 23 = \frac{1}{3} \pi 490000 \times 23$$ 4. **Step 2:** Calculate: $$V = \frac{1}{3} \pi 11270000 = 3756666.7\pi \approx 11800000.5\text{ cm}^3$$ --- 1. **Problem:** Find volume of composite figure: hemisphere radius 5 in and cone height 10 in radius 5 in. 2. **Formula:** Hemisphere volume: $$V_h = \frac{2}{3} \pi r^3$$ Cone volume: $$V_c = \frac{1}{3} \pi r^2 h$$ 3. **Step 1:** Hemisphere volume: $$V_h = \frac{2}{3} \pi 5^3 = \frac{2}{3} \pi 125 = \frac{250}{3} \pi$$ 4. **Step 2:** Cone volume: $$V_c = \frac{1}{3} \pi 5^2 \times 10 = \frac{1}{3} \pi 25 \times 10 = \frac{250}{3} \pi$$ 5. **Step 3:** Total volume: $$V = V_h + V_c = \frac{250}{3} \pi + \frac{250}{3} \pi = \frac{500}{3} \pi \approx 523.6\text{ in}^3$$ --- 1. **Problem:** Find volume of hemisphere bowl diameter 12 inches. 2. **Formula:** Hemisphere volume: $$V = \frac{2}{3} \pi r^3$$ 3. **Step 1:** Radius: $$r = \frac{12}{2} = 6\text{ in}$$ 4. **Step 2:** Volume: $$V = \frac{2}{3} \pi 6^3 = \frac{2}{3} \pi 216 = 144\pi \approx 452.4\text{ in}^3$$ --- 1. **Problem:** Find volume of composite figure: cylinder radius 7 m height 25 m, cone radius 7 m height 10 m. 2. **Formula:** Cylinder volume: $$V_c = \pi r^2 h$$ Cone volume: $$V_{cone} = \frac{1}{3} \pi r^2 h$$ 3. **Step 1:** Cylinder volume: $$V_c = \pi 7^2 \times 25 = 1225\pi$$ 4. **Step 2:** Cone volume: $$V_{cone} = \frac{1}{3} \pi 7^2 \times 10 = \frac{490}{3} \pi$$ 5. **Step 3:** Total volume: $$V = 1225\pi + \frac{490}{3} \pi = \frac{3675 + 490}{3} \pi = \frac{4165}{3} \pi \approx 4360.3\text{ m}^3$$ --- 1. **Problem:** Find volume of cone B which is 3 times size of cone A with radius 3 m height 8 m. 2. **Formula:** Volume of cone A: $$V_A = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi 3^2 \times 8 = 24\pi$$ 3. **Step 1:** Volume of cone B: $$V_B = 3 \times V_A = 72\pi \approx 226.2\text{ m}^3$$ --- 1. **Problem:** Find difference in volume between cylinder canister (height 10 in radius 2 in) and soup can (14 in³). 2. **Formula:** Cylinder volume: $$V = \pi r^2 h$$ 3. **Step 1:** Cylinder volume: $$V = \pi 2^2 \times 10 = 40\pi \approx 125.7\text{ in}^3$$ 4. **Step 2:** Difference: $$125.7 - 14 = 111.7\text{ in}^3$$ --- 1. **Problem:** Find volume of gravel pile shaped as cone with height 8 ft and diameter 12 ft. 2. **Formula:** Volume of cone: $$V = \frac{1}{3} \pi r^2 h$$ 3. **Step 1:** Radius: $$r = \frac{12}{2} = 6\text{ ft}$$ 4. **Step 2:** Volume: $$V = \frac{1}{3} \pi 6^2 \times 8 = \frac{1}{3} \pi 36 \times 8 = 96\pi \approx 301.6\text{ ft}^3$$