Number 31 Calc 3 help please Changes in torus surface area The surface area of a

Question

Number 31 Calc 3 help please Changes in torus surface area The surface area of a torus (an ideal bagel or doughnut) with an inner radius r and an outer R > r is S = 4 pi 2(R2 - r2). If r increases and R decreases. docs S increase or decrease or is it impossible to say? If r increases and R increase does S increase or decrease, or is it impossible to say? Estimate the change in the surface area of the torus when r changes from r = 3.00 to r 3.05 and R changes from R = 5.50 to R = 5.65. Estimate the change in the surface area of the torus when r changes from r = 3.00 to r = 2.95 and R changes from R = 7.00 to R = 7.04. Find the relationship between the changes in r and R that leaves the surface area (approximately) unchanged.

Explanation / Answer

S = 4 pi (R2-r2)

dS = 8 pi (RdR-rdr) ..Eqn 1

a)

Given dr> 0 and dR <0

So from Eqn 1 dS < 0

So, S decreases

b)

Given dr>0 and dR >0

So from Eqn 1 can't comment about dS

So, it is impossible to say

c)

dr = 3.05 - 3 = 0.05

dR=5.65 - 5.50 = 0.15

dS= 8 pi ( 5.5 X 0.15 - 3 X 0.05) = 16.96

d)

dr = 2.95-3 = - 0.05

dR=7.04 - 7 = 0.04

dS= 8 pi ( 7 X 0.04 + 3 X 0.05) = 10.8

e)

dS=0 = 8 pi ( RdR-rdr)

dR/dr=r/R

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

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