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A stone is dropped in a pond which causes circular ripples. The radius
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11 Aug 2025, 09:59
11 Aug 2025, 09:59
Expert Reply
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Question Stats:
80% (01:30) correct
20% (01:05) wrong based on 5 sessions
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A stone is dropped in a pond which causes circular ripples. The radius of the ripple increases by $x$ inches every second. If after 10 seconds the area enclosed by the circular ripple is $\(400 \pi\)$ square inches. What is the value of $x$ ?
(A) 2
(B) 4
(C) $\(\sqrt{200}\)$
(D) $\(\sqrt{300}\)$
(E) $\(\sqrt{400}\)$
(A) 2
(B) 4
(C) $\(\sqrt{200}\)$
(D) $\(\sqrt{300}\)$
(E) $\(\sqrt{400}\)$
Re: A stone is dropped in a pond which causes circular ripples. The radius
[#permalink]
30 Aug 2025, 05:55
30 Aug 2025, 05:55
Expert Reply
Given:
- Radius increases by $x$ inches every second.
- After 10 seconds, the area of the circular ripple is $\(400 \pi\)$ square inches.
The area $A$ of a circle is:
$$
\(A=\pi r^2\)
$$
Radius after 10 seconds $\(r=10 x\)$ (since it grows by $x$ inches per second).
So,
$$
\(400 \pi=\pi(10 x)^2\)
$$
Divide both sides by $\(\pi\)$ :
$$
\(400=100 x^2\)
$$
Solving for $\(x^2\)$ :
$$
\(x^2=\frac{400}{100}=4\)
$$
So,
$$
\(x=\sqrt{4}=2\)
$$
The value of $x$ is 2 inches per second.
The correct answer is (A) 2 .
- Radius increases by $x$ inches every second.
- After 10 seconds, the area of the circular ripple is $\(400 \pi\)$ square inches.
The area $A$ of a circle is:
$$
\(A=\pi r^2\)
$$
Radius after 10 seconds $\(r=10 x\)$ (since it grows by $x$ inches per second).
So,
$$
\(400 \pi=\pi(10 x)^2\)
$$
Divide both sides by $\(\pi\)$ :
$$
\(400=100 x^2\)
$$
Solving for $\(x^2\)$ :
$$
\(x^2=\frac{400}{100}=4\)
$$
So,
$$
\(x=\sqrt{4}=2\)
$$
The value of $x$ is 2 inches per second.
The correct answer is (A) 2 .
gmatclubot
Re: A stone is dropped in a pond which causes circular ripples. The radius [#permalink]
30 Aug 2025, 05:55
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