1. **Problem Statement:** We are given two cylinders: - Cylinder A: Diameter = 7 cm, Height = 14 cm - Cylinder B: Diameter = 14 cm, Height = 7 cm We need to compare their volumes and verify which has a greater volume. Then check if the cylinder with the greater volume also has a greater surface area. 2. **Step 1: Volume Formula for Cylinder:** The volume $V$ of a cylinder is given by $$ V = \pi r^2 h $$ where $r$ is the radius and $h$ is the height. 3. **Step 2: Calculate radius for both cylinders:** - Cylinder A radius, $r_A = \frac{7}{2} = 3.5$ cm - Cylinder B radius, $r_B = \frac{14}{2} = 7$ cm 4. **Step 3: Calculate volumes:** - Volume of Cylinder A: $$ V_A = \pi (3.5)^2 \times 14 = \pi \times 12.25 \times 14 = 171.5\pi \text{ cm}^3 $$ - Volume of Cylinder B: $$ V_B = \pi (7)^2 \times 7 = \pi \times 49 \times 7 = 343\pi \text{ cm}^3 $$ 5. **Step 4: Compare volumes:** $$ V_B = 343\pi > V_A = 171.5\pi $$ Thus, Cylinder B has a greater volume. 6. **Step 5: Surface Area Formula for Cylinder:** The total surface area $S$ of a cylinder is $$ S = 2\pi r(h + r) $$ 7. **Step 6: Calculate surface areas:** - Surface area of Cylinder A: $$ S_A = 2\pi \times 3.5 \times (14 + 3.5) = 7\pi \times 17.5 = 122.5\pi \text{ cm}^2 $$ - Surface area of Cylinder B: $$ S_B = 2\pi \times 7 \times (7 + 7) = 14\pi \times 14 = 196\pi \text{ cm}^2 $$ 8. **Step 7: Compare surface areas:** $$ S_B = 196\pi > S_A = 122.5\pi $$ Cylinder B also has the greater surface area. **Final Answer:** Cylinder B, which has diameter 14 cm and height 7 cm, has both the greater volume and the greater surface area compared to Cylinder A.