To determine if the two cylinders have the same surface area, we need to calculate the surface area of Cylinder A using the following formulas:
-
Area of each circular face:
\[ \text{Area} = \pi r^2 \] -
Total area of the circular faces:
\[ \text{Total Area} = 2 \times \text{Area of each circular face} \] -
Circumference of the circular face:
\[ \text{Circumference} = 2 \pi r \] -
Area of the lateral face (side area):
\[ \text{Area of Lateral Face} = \text{Circumference} \times \text{Height} \] -
Total Surface Area:
\[ \text{Total Surface Area} = \text{Total Area of Circular Faces} + \text{Area of Lateral Face} \]
Using this information, we need to plug in the values for the radius and height of Cylinder A to perform the calculations.
Let's assume:
- Radius of Cylinder A, \( r_A = R \) (to be determined)
- Height of Cylinder A, \( h_A = H \) (to be determined)
Now we can summarize the values accordingly:
- \( \text{Radius of Cylinder A} = R \) inches
- \( \text{Area of Each Circular Face of Cylinder A} = 3.14 \times R^2 \) square inches
- \( \text{Total Area of the Circular Faces of Cylinder A} = 2 \times (3.14 \times R^2) = 6.28R^2 \) square inches
- \( \text{Circumference of Cylinder A} = 2 \times 3.14R = 6.28R \) inches
- \( \text{Height of Cylinder A} = H \) inches
- \( \text{Area of the Lateral Face of Cylinder A} = 6.28R \times H = 6.28RH \) square inches
- \( \text{Total Surface Area of Cylinder A} = 6.28R^2 + 6.28RH = 6.28(R^2 + RH) \) square inches
Next, we need to compare the total surface area of Cylinder A to the surface area of Cylinder B, which is given as 251.2 square inches.
To answer Question 2, we can set the equation:
\[ 6.28(R^2 + RH) \stackrel{?}{=} 251.2 \]
Without the specific values for \( R \) and \( H \), we can't determine if the two surface areas are equal. However, if you provide the values of the radius and height of Cylinder A, I can calculate the total surface area and compare it with the surface area of Cylinder B.