💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Get the answer to your homework problem.

Try Numerade Free for 7 Days

The radius of a spherical ball is increasing at a rate of $ 2 cm/min. $ At what rate is the surface area of the ball increasing when the radius is $ 8 cm? $

$128 \pi \mathrm{cm}^{2} / \mathrm{min}$

03:03

Alex L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Campbell University

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

03:07

In Exercises $5-8,$ assume…

02:19

The radius of a sphere is …

01:04

03:49

The area of a circle incre…

Volume of Sphere What is t…

04:15

The volume $V$ of a sphere…

02:05

A spherical balloon is inf…

02:47

A circle has a radius of 8…

04:30

The radius of an inflating…

03:10

Volume The radius $r$ of a…

we're told that the radius of hysterical ball is increasing at a rate of two centimeters per minute. So if we call the Radius, are in time T we have that d R D t is equal to positive, too, and were asked at what rate the surface area of the ball was increasing and the radius is eight centimeters. So are the radius is eight to determine the rate at which the surface area goal is increasing. First, it's fine what the surface area is in terms of the radius of the spiritual ball. So we know that the surface area of a bull this is four pi r squared and therefore we have the rate of change of the surface area with respective time. This is the SPT and by the chain rule. This is eight pi r times d r d t. And so, in the context of this problem, when R is equal to eight and be our duty is to this is a pie times eight times two, which is 128th pie. I don't know. It's from three, and this is the rate of change of the surface area surface area is in this case, square centimeters and the time is in minutes. So this is 128 high square, centimeters per minute. I'm so mad.

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

In Exercises $5-8,$ assume that the radius $r$ of a sphere is expanding at a…

The radius of a sphere is increasing at a rate of $ 4 mm/s. $ How fast is th…

The radius of a sphere is increasing at a rate of 4 $\mathrm{mm} / \mathrm{s…

The area of a circle increases at a rate of$1 \mathrm{cm}^{2} / \mathrm{…

Volume of Sphere What is the rate of change of the volume of a sphere with r…

The volume $V$ of a sphere of radius $r$ changes over time $t$a. Find an…

A spherical balloon is inflated and its volume increases at a rate of 15 in …

A circle has a radius of 8 in. Find the increase in area when the radius is …

The radius of an inflating balloon A spherical balloon is inflated with heli…

Volume The radius $r$ of a sphere is increasing at a rate of 3 inches per mi…