To determine the amount of icing needed to cover the sides and top of the cylindrical cake, we need to calculate the surface area of the sides and the top of the cylinder.
The formulas we will use are:
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Lateral surface area of the cylinder (sides): \[ \text{Lateral Surface Area} = 2 \pi r h \] where \( r \) is the radius and \( h \) is the height of the cylinder.
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Area of the top of the cylinder: \[ \text{Area of the Top} = \pi r^2 \]
Given:
- Radius \( r = 5 \) inches
- Height \( h = 7 \) inches
- \( \pi \) is approximated as \( 3.14 \)
Step 1: Calculate the Lateral Surface Area
\[ \text{Lateral Surface Area} = 2 \times 3.14 \times 5 \times 7 \] \[ = 2 \times 3.14 \times 35 \] \[ = 6.28 \times 35 \] \[ = 219.8 \text{ square inches} \]
Step 2: Calculate the Area of the Top
\[ \text{Area of the Top} = 3.14 \times (5^2) \] \[ = 3.14 \times 25 \] \[ = 78.5 \text{ square inches} \]
Step 3: Total Surface Area to be Iced
\[ \text{Total Area} = \text{Lateral Surface Area} + \text{Area of the Top} \] \[ = 219.8 + 78.5 \] \[ = 298.3 \text{ square inches} \]
Final Result
The total area of icing needed to cover the sides and the top of the cake is 298.3 square inches.
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