Let's solve each question step by step.
Given:
- Diameter of the cake: 8 inches
- Height of the cake: 10 inches
Question 1:
Calculate the radius: \[ \text{radius} = \frac{\text{diameter}}{2} = \frac{8 , \text{inches}}{2} = 4 , \text{inches} \] Answer: 4 inches
Question 2:
Area of the top circular base: \[ \text{area} = \pi r^2 = 3.14 \times (4 , \text{inches})^2 = 3.14 \times 16 = 50.24 , \text{square inches} \] Answer: 50.24 square inches
Question 3:
Area of the bottom circular base: (It’s identical to the top circular base) \[ \text{area} = 50.24 , \text{square inches} \] Answer: 50.24 square inches
Question 4:
Total area of circular bases (add the areas): \[ \text{total area of circular bases} = \text{area of top} + \text{area of bottom} = 50.24 + 50.24 = 100.48 , \text{square inches} \] Answer: 100.48 square inches
Question 5:
Circumference of the circular base: \[ \text{circumference} = 2 \pi r = 2 \times 3.14 \times 4 , \text{inches} = 25.12 , \text{inches} \] Answer: 25.12 square inches (Note: The circumference is in inches, not square inches)
Question 6:
Height of the cylinder:
- Given height = 10 inches Answer: 10 inches
Question 7:
Area of the lateral face (circumference x height): \[ \text{area of the lateral face} = \text{circumference} \times \text{height} = 25.12 \times 10 = 251.2 , \text{square inches} \] Answer: 251.2 square inches
Question 8:
Find the surface area of the cylinder: \[ \text{Surface Area} = \text{total area of circular bases} + \text{area of lateral rectangular face} \] \[ \text{Surface Area} = 100.48 + 251.2 = 351.68 , \text{square inches} \] Answer: 351.68 (total area of circular bases) + 251.2 (area of lateral rectangular face) = 351.68 square inches