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.(1 point)
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To find the surface area of the sides of the cake, we need to find the circumference of the base of the cake and multiply it by the height of the cake. The circumference of the base is given by the formula:
C = 2πr
Where r is the radius of the cake. We can substitute the given values to find the circumference:
C = 2 * 3.14 * 5 = 31.4 inches
Now, we can find the surface area of the sides of the cake by multiplying the circumference by the height:
Sides surface area = C * height = 31.4 * 7 = 219.8 square inches
To find the surface area of the top of the cake, we need to find the area of a circle with the radius of the cake and multiply it by 2 since there are 2 circular tops. The area of a circle is given by the formula:
A = πr^2
Substituting the given values, we find:
A = 3.14 * 5^2 = 3.14 * 25 = 78.5 square inches
Now, we can find the total surface area of the cake by adding the surface area of the sides and the top:
Total surface area = Sides surface area + 2 * Top surface area = 219.8 + 2 * 78.5 = 376.8 square inches
Therefore, approximately 376.8 square inches of icing will be needed to cover the sides and top of the cake.