Question

A baker needs to cover a cylinder cake with icing. The cake has a radius of 5 inches and a height of 7 inches. How many square inches of icing will be needed to cover the sides and top of the cake? Icing will not be added to the bottom of the cake. Use 3.14 for pi and round your answer to the nearest tenth.

Answer 1

To calculate the total surface area of the cylinder cake that needs icing, we need to find the area of the sides and the top of the cylinder.

1. Area of the sides (lateral surface area): The formula for the lateral surface area of a cylinder is given by: \[ \text{Lateral Surface Area} = 2 \pi r h \] where:

   • \( r \) is the radius of the cylinder,
   • \( h \) is the height of the cylinder.

   Plugging in the values:

   • \( r = 5 \) inches,
   • \( h = 7 \) inches,
   • \( \pi \approx 3.14 \).

   \[ \text{Lateral Surface Area} = 2 \times 3.14 \times 5 \times 7 \] \[ \text{Lateral Surface Area} = 2 \times 3.14 \times 35 \] \[ \text{Lateral Surface Area} = 2 \times 109.9 \] \[ \text{Lateral Surface Area} = 219.8 \text{ square inches} \]

2. Area of the top of the cake: The area of the top (which is a circle) is given by: \[ \text{Top Area} = \pi r^2 \]

   Plugging in the values: \[ \text{Top Area} = 3.14 \times 5^2 \] \[ \text{Top Area} = 3.14 \times 25 \] \[ \text{Top Area} = 78.5 \text{ square inches} \]

3. Total area to be iced: Now, we add the lateral surface area and the top area together: \[ \text{Total Area} = \text{Lateral Surface Area} + \text{Top Area} \] \[ \text{Total Area} = 219.8 + 78.5 \] \[ \text{Total Area} = 298.3 \text{ square inches} \]

Finally, rounding our answer to the nearest tenth, we find that the amount of icing needed to cover the sides and top of the cake is: \[ \boxed{298.3} \text{ square inches} \]