Skip to content

Area growth of a pond ripple after ten seconds

Question

A circular ripple spreads out on a pond, its radius growing at 22 ft per second from zero. After 1010 seconds the ripple's area is increasing at kπk\pi square feet per second for an integer kk. What is kk?

Short answer

k=80k=80. After 1010 s the radius is 2020 ft. From A=πr2A=\pi r^2, A′=2πrr′=2π⋅20⋅2=80πA'=2\pi rr'=2\pi\cdot20\cdot2=80\pi.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question