To determine how much icing the baker needs to cover the sides and the top of the cylinder cake, we first need to calculate the surface area that needs to be covered.
The formula for the lateral surface area (sides) of a cylinder is:
\[ \text{Lateral Surface Area} = 2 \pi r h \]
The formula for the area of the top (which is a circle) of a cylinder is:
\[ \text{Area of the Top} = \pi r^2 \]
Given:
- Radius \( r = 5 \) inches
- Height \( h = 7 \) inches
- Pi \( \pi = 3.14 \)
Step 1: Calculate the lateral surface area
\[ \text{Lateral Surface Area} = 2 \cdot 3.14 \cdot 5 \cdot 7 \] \[ = 2 \cdot 3.14 \cdot 35 \] \[ = 2 \cdot 109.9 \] \[ = 219.8 \text{ square inches} \]
Step 2: Calculate the area of the top
\[ \text{Area of the Top} = 3.14 \cdot (5^2) \] \[ = 3.14 \cdot 25 \] \[ = 78.5 \text{ square inches} \]
Step 3: Total area to cover
Now, add the lateral surface area and the area of the top: \[ \text{Total Area} = \text{Lateral Surface Area} + \text{Area of the Top} \] \[ = 219.8 + 78.5 \] \[ = 298.3 \text{ square inches} \]
Final Answer
The baker will need approximately 298.3 square inches of icing to cover the sides and top of the cake.
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