The volume V = 4/3 pi r^3 of a spherical balloon changes with the radius. At wha

Question

The volume V = 4/3 pi r^3 of a spherical balloon changes with the radius. At what rate (in^3/in) does the volume change with respect to the radius when r = 8 in? Using the rate from part a, by approximately how much does the volume increase when the radius changes from 8 to 8.5 in? At what rate (in^3/in) does the volume change with respect to the radius when r = 8 in? in^3/in (Type an exact answer in terms of pi.) Using the rate from part a. by approximately how much does the volume increase when the radius changes from 8 to 8.5 in? in^3 (Use the answer from part a to find this answer. Round to two decimal places as needed.)

Explanation / Answer

a) V =(4/3)pi*r3

hence rate of change of volume =dV/dr =4*pi*r2

at r=8; change in volume ; dV/dt =4*22/7*(8)2 =804.5714

b) change in volume =(4/3)pi(r13 -r23) =427.9524

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.