2019 AMC 12A Problems/Problem 1

Problem

The area of a pizza with radius $4$ is $N$ percent larger than the area of a pizza with radius $3$ inches. What is the integer closest to $N$ ?

$\textbf{(A) } 25 \qquad\textbf{(B) } 33 \qquad\textbf{(C) } 44\qquad\textbf{(D) } 66 \qquad\textbf{(E) } 78$

Solution

Let the first jar's volume be $A$ and the second's be $B$ . It is given that $\frac{3}{4}A=\frac{5}{6}B$ . We find that $\frac{B}{A}=\frac{3/4}{5/6}=\boxed{\frac{9}{10}}.$ We know that this is the ratio of smaller to larger volume already because it is less than $1.$

2019 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

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2019 AMC 12A Problems/Problem 1

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