To determine if the student is correct about the surface areas of the two cylinders, let's start with the necessary calculations for Cylinder A. We'll use the following formulas related to cylinders:
- Area of one circular face: \( A = \pi r^2 \)
- Total area of the circular faces: \( A_{total} = 2 \pi r^2 \) (since a cylinder has two circular faces)
- Circumference of the base: \( C = 2 \pi r \)
- Area of the lateral face: \( A_{lateral} = C \times h = 2 \pi r h \)
- Total Surface Area: \( A_{total_surface} = A_{total} + A_{lateral} = 2 \pi r^2 + 2 \pi r h \)
Now, we need some specific values for the radius and height of Cylinder A in order to perform the calculations.
Assuming you have the values for the radius \( r \) and height \( h \) of Cylinder A, fill them in, and calculate as follows:
- Radius of Cylinder A: \( r = \text{[value in inches]} \)
- Area of ONE Circular Face of Cylinder A: \[ A = 3.14 \times r^2 \]
- Total Area of the Circular Faces of Cylinder A: \[ Total_A_{circular} = 2 \times A = 2 \times (3.14 \times r^2) \]
- Circumference of Cylinder A: \[ C = 2 \times 3.14 \times r \]
- Height of Cylinder A: \( h = \text{[value in inches]} \)
- Area of the Lateral Face of Cylinder A: \[ A_{lateral} = C \times h = (2 \times 3.14 \times r) \times h \]
- Total Surface Area of Cylinder A: \[ A_{total_surface} = Total_A_{circular} + A_{lateral} = (2 \times 3.14 \times r^2) + ((2 \times 3.14 \times r) \times h) \]
Now you fill in the actual values for Cylinder A, and then you can calculate the total surface area.
Finally, compare the total surface area of Cylinder A with the surface area of Cylinder B:
Question 2: The surface area of Cylinder A (is less than/equal to/greater than) the surface area of Cylinder B.
Make sure to fill in the specifics for Cylinder A so the calculations are correctly executed. If you provide the radius and height, I can help you with the specifics of the calculations!