Answer:
To find the surface area of the cake that needs to be covered with icing, we need to calculate the combined area of the sides and top of the cylinder.
1. Calculate the area of the sides of the cylinder:
- The formula for the lateral surface area of a cylinder is 2πrh, where π is a mathematical constant (approximately 3.14), r is the radius, and h is the height.
- In this case, the radius (r) is 5 inches and the height (h) is 7 inches.
- Substituting these values into the formula: 2 x 3.14 x 5 x 7 = 219.8 square inches.
2. Calculate the area of the top of the cylinder:
- The formula for the area of a circle is πr^2, where r is the radius.
- In this case, the radius (r) is 5 inches.
- Substituting this value into the formula: 3.14 x (5^2) = 78.5 square inches.
3. Add the area of the sides and the area of the top to get the total surface area that needs to be covered with icing:
- 219.8 + 78.5 = 298.3 square inches.
Therefore, approximately 298.3 square inches of icing will be needed to cover the sides and top of the cake.
Explanation: