If 20 circular pepperoni slices each with a 1 inch-diameter cover a circular pizza pie with diameter 14 inches, what fraction of the pizza is covered with pepperoni slices?
a)5/49
b)3/49
c)7/49
d)6/79
e)9/79
Answer is a.
Need help in solution.
Geometry
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Fraction Of Area Of Pizza That Is Covered By Pepperoni = Total Area Of Pepperoni Slices/Total Area Of Pizza
Area Of One Pepperoni Slice = πr² = π(1/2)² = π/4
Area Of All 20 Pepperoni Slices = 20 * π/4 = 5π
Area Of Pizza = πr² = π7² = 49π
Fraction Of Area Of Pizza That Is Covered By Pepperoni = 5Ï€/49Ï€ = 5/49
The correct answer is A.
Area Of One Pepperoni Slice = πr² = π(1/2)² = π/4
Area Of All 20 Pepperoni Slices = 20 * π/4 = 5π
Area Of Pizza = πr² = π7² = 49π
Fraction Of Area Of Pizza That Is Covered By Pepperoni = 5Ï€/49Ï€ = 5/49
The correct answer is A.
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Slices / Pie =>
20 * ((half-diameter of slice)² * π) / ((half-diameter of pie)² * π)
20 * (.5² * π) / (7² * π) =>
20 * .25 * π / 49π =>
5/49
20 * ((half-diameter of slice)² * π) / ((half-diameter of pie)² * π)
20 * (.5² * π) / (7² * π) =>
20 * .25 * π / 49π =>
5/49