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Chapter 5: Q. 65 (page 257)

The surface area S (in square meters) of a hot-air balloon is given by S(r)=4蟺谤2, where ris the radius of the balloon (in meters).If the radius ris increasing with time t(in seconds) according to the formula r(t)=23t3,t鈮�0, find the surface area S of the balloon as a function of the timet.

Short Answer

Expert verified

S(t)=169蟺迟6.

Step by step solution

01

Step 1. Given Information

Given thatS(r)=4蟺谤2andr(t)=23t3,t鈮�0.

02

Step 2. Solution

We have to find surface area Sof the balloon as a function of time t.

We have S(r)is function of rand r(t) is function of t.

So, we have to find S鈭�r(t).

Now,

S鈭�r(t)=S(r(t))S鈭�r(t)=4蟺{r(t)}2 S鈭�r(t)=4蟺23t32S鈭�r(t)=4蟺49t6S鈭�r(t)=169蟺迟6.

03

Step3. Final Answer

Hence, S as a function of t isS(t)=169蟺迟6.

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