if-a-snowball-melts-so-that-its-surface-area-decreases-at-a-rate-of-1cm2min-find-the-rate-at-which-t

Question

If a snowball melts so that its surface area decreases at a rate of $ 1cm^2/min, $ find the rate at which the diameter decreases when the diameter is $ 10 cm. $
(a) What quantities are given in the problem?
(b) What is the unknown?
(c) Draw a picture of the situation for any time $ t. $
(d) Write an equation that relates the quantities.
(e) Finish solving the problem.

Wen Zheng · Accepted Answer

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Problem

A street light mounted at the top of a $ 15-ft-ta…

Problem 14 Easy Difficulty

Answer

a) 1 $\mathrm{cm}^{2} / \mathrm{min}$ and 10 $\mathrm{cm}$
b) the rate that the diameter is decreasing when the diameter is 10 $\mathrm{cm}$
c) See step for answer
d) $\pi \ell^{2}$
e) Diameter is decreasing at a rate of $\frac{1}{20 \pi} \approx 0.016 \mathrm{cm} / \mathrm{min}$

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a) 1 $\mathrm{cm}^{2} / \mathrm{min}$ and 10 $\mathrm{cm}$b) the rate that the diameter is decreasing when the diameter is 10 $\mathrm{cm}$c) See step for answerd) $\pi \ell^{2}$e) Diameter is decreasing at a rate of $\frac{1}{20 \pi} \approx 0.016 \mathrm{cm} / \mathrm{min}$

Calculus: Early Transcendentals

Catherine R.

Heather Z.

Kayleah T.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Catherine R.

Caleb E.

Kristen K.

Joseph L.

a) 1 $\mathrm{cm}^{2} / \mathrm{min}$ and 10 $\mathrm{cm}$
b) the rate that the diameter is decreasing when the diameter is 10 $\mathrm{cm}$
c) See step for answer
d) $\pi \ell^{2}$
e) Diameter is decreasing at a rate of $\frac{1}{20 \pi} \approx 0.016 \mathrm{cm} / \mathrm{min}$