Let's complete the steps to determine the surface area of Mary's cake, which is shaped like a cylinder.
Step 1: Find the radius.
- Given the diameter is 8 inches, the radius (r) can be calculated as: \[ \text{radius} = \frac{\text{diameter}}{2} = \frac{8}{2} = 4 \text{ inches} \]
Question 2: Area of the top circular base.
- The area (A) of a circle is given by the formula \( A = \pi r^2 \). \[ \text{Area of the top circular base} = 3.14 \times (4^2) = 3.14 \times 16 = 50.24 \text{ square inches} \]
Question 3: Area of the bottom circular base.
- Since the bottom circular base is the same as the top circular base: \[ \text{Area of the bottom circular base} = 50.24 \text{ square inches} \]
Question 4: Total area of circular bases.
- Add the areas of the top and bottom bases: \[ \text{Total area of circular bases} = 50.24 + 50.24 = 100.48 \text{ square inches} \]
Question 5: Circumference of the circular base.
- The circumference (C) of a circle is given by the formula \( C = 2\pi r \). \[ \text{Circumference of the circular base} = 2 \times 3.14 \times 4 = 25.12 \text{ inches} \]
Question 6: Height of the cylinder.
- The height \( h \) is given as 10 inches.
Question 7: Area of the lateral face.
- The area of the lateral face (L) can be calculated as: \[ L = \text{Circumference} \times \text{Height} = 25.12 \times 10 = 251.2 \text{ square inches} \]
Question 8: Find the Surface Area of the cylinder.
- The surface area (SA) of the cylinder is: \[ \text{Surface Area} = \text{Total area of circular bases} + \text{Area of lateral rectangular face} \] \[ \text{Surface Area} = 100.48 + 251.2 = 351.68 \text{ square inches} \]
Final Answers
- radius = 4 inches
- area of the top circular base = 50.24 square inches
- area of the bottom circular base = 50.24 square inches
- total area of circular bases = 100.48 square inches
- circumference of the circular base = 25.12 inches
- height of the cylinder = 10 inches
- area of the lateral face = 251.2 square inches
- Surface Area = 351.68 square inches