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The surface area of a hot-air balloon is given by the function S(r) 4Tr", where r is the radius of the 3 -ť°, find 4 balloon in meters. If the radius r is increasing with time t (in seconds) by the function r(t) the surface area S of the balloon as it relates to time.

The surface area of a hot-air balloon is given by the function S(r) 4Tr", where r is the radius of the 3 -ť°, find 4 balloon in meters. If the radius r is increasing with time t (in seconds) by the function r(t) the surface area S of the balloon as it relates to time.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.6: Solving Quadratic Equations By Using The Quadratic Formula
Problem 64PFA
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The surface area of a hot-air balloon is given by the function S(r) = 4rr°, where r is the radius of the 3 balloon in meters. If the radius r is increasing with time t (in seconds) by the function r(t) t°, find 4 the surface area S of the balloon as it relates to time.
Transcribed Image Text:The surface area of a hot-air balloon is given by the function S(r) = 4rr°, where r is the radius of the 3 balloon in meters. If the radius r is increasing with time t (in seconds) by the function r(t) t°, find 4 the surface area S of the balloon as it relates to time.
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the radius is increasing at a rate of 

r=\frac{3}{4}t^2

the surface area is given by

S=4\pi r^2

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