To find the amount of icing needed to cover the sides and top of the cylindrical cake, we can calculate the surface area of the cylinder excluding the bottom base.
The formula for the surface area \(A\) of a cylinder is given by:
\[ A = 2\pi rh + \pi r^2 \]
Where:
- \(r\) is the radius of the cylinder
- \(h\) is the height of the cylinder
In this case, we are only covering the sides and the top of the cylinder, so we need to consider the lateral surface area plus the area of the top circle:
-
Lateral Surface Area: \[ \text{Lateral Surface Area} = 2\pi rh \]
-
Area of the Top: \[ \text{Area of the Top} = \pi r^2 \]
Thus, the total surface area that needs icing will be: \[ \text{Total Surface Area} = 2\pi rh + \pi r^2 \]
Now plug in the values:
- \(r = 5\) inches
- \(h = 7\) inches
- \(\pi = 3.14\)
Step 1: Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 5 \times 7 \] \[ = 2 \times 3.14 \times 35 \] \[ = 6.28 \times 35 \] \[ = 219.8 \text{ square inches} \]
Step 2: Calculate the area of the top: \[ \pi r^2 = 3.14 \times 5^2 \] \[ = 3.14 \times 25 \] \[ = 78.5 \text{ square inches} \]
Step 3: Add the lateral surface area and top area: \[ \text{Total Surface Area} = 219.8 + 78.5 \] \[ = 298.3 \text{ square inches} \]
Therefore, the baker will need 298.3 square inches of icing to cover the sides and top of the cake.