To determine if the two cylinders have the same surface area, we will calculate the surface area of Cylinder A using the provided dimensions.
Given for Cylinder A:
- Height (h) = 10 inches
- Diameter = 3 inches
- Radius (r) = Diameter / 2 = 3 inches / 2 = 1.5 inches
Step 1: Calculate the Area of One Circular Face
The area \( A_c \) of one circular face of a cylinder is given by the formula: \[ A_c = \pi r^2 \] Substituting \( \pi = 3.14 \) and \( r = 1.5 \): \[ A_c = 3.14 \times (1.5)^2 = 3.14 \times 2.25 = 7.065 \text{ square inches} \]
Step 2: Total Area of the Circular Faces
Since there are two circular faces: \[ \text{Total Area of Circular Faces} = 2 \times A_c = 2 \times 7.065 = 14.13 \text{ square inches} \]
Step 3: Calculate the Circumference of Cylinder A
The circumference \( C \) of the base of the cylinder is given by: \[ C = 2\pi r \] Substituting \( r = 1.5 \): \[ C = 2 \times 3.14 \times 1.5 = 9.42 \text{ inches} \]
Step 4: Calculate the Area of the Lateral Face
The area \( A_l \) of the lateral face of the cylinder is given by: \[ A_l = C \times h \] Substituting \( C = 9.42 \) and \( h = 10 \): \[ A_l = 9.42 \times 10 = 94.2 \text{ square inches} \]
Step 5: Total Surface Area of Cylinder A
The total surface area \( A_s \) of the cylinder is given by: \[ A_s = \text{Total Area of Circular Faces} + \text{Area of Lateral Face} \] Substituting the values: \[ A_s = 14.13 + 94.2 = 108.33 \text{ square inches} \]
Summary of Results for Cylinder A:
- Radius of Cylinder A = 1.5 inches
- Area of ONE Circular Face of Cylinder A = 7.065 square inches
- Total Area of the Circular Faces of Cylinder A = 14.13 square inches
- Circumference of Cylinder A = 9.42 inches
- Height of Cylinder A = 10 inches
- Area of the Lateral Face of Cylinder A = 94.2 square inches
- Total Surface Area of Cylinder A = 108.33 square inches
Question 2
Now we can compare the surface area of Cylinder A to that of Cylinder B.
The surface area of Cylinder B = 251.2 square inches.
The surface area of Cylinder A (108.33 square inches) is less than the surface area of Cylinder B (251.2 square inches).
Final Answer:
The statement regarding the surface area of Cylinder A compared to Cylinder B is: The surface area of Cylinder A is less than the surface area of Cylinder B.