The surface area S of a sphere of radius r feet is S = S(r) = 4πr^2. Find the instantaneous rate of change of surface area with respect to r at r=4. Show work please.
2007-05-20 05:29:09 · 5 answers · asked by Anna D 1 in Science & Mathematics ➔ Mathematics
RTF: dS / dr when r = 4
dS/dr = 8*pi*r = 32*pi when r = 4
2007-05-20 05:32:23 · answer #1 · answered by Dr D 7 · 3⤊ 0⤋
S(r) = 4πr²
S `(r) = ds/dr = 8 π r
S `(4) = 32 π = 101 ft² / s
2007-05-20 08:37:10 · answer #2 · answered by Como 7 · 0⤊ 0⤋
Differentiate with respect to r
d/dr (4πr^2) = 4π (2r) dr
2007-05-20 05:34:19 · answer #3 · answered by apjok 3 · 0⤊ 0⤋
this is by definition ds/dr = 8pir and at r =4 is 32pi
2007-05-20 05:32:50 · answer #4 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
dS/dr = S'(r) = 4π(2) r = 8πr
S'(4) = 8π(4) = 32π
2007-05-20 05:35:22 · answer #5 · answered by hawkeye3772 4 · 1⤊ 0⤋