rate of change quesion ? (1 Viewer)

[jkingx]

A spherical balloon with radius r cm is being deflated.
1) show that the rate of change of the surface area with respect to the radius is proportional to the radius.
2) find the rate of change of the surface area when r = 5cm

 

[Prashant Sallan]

A spherical balloon with radius r cm is being deflated.
1) show that the rate of change of the surface area with respect to the radius is proportional to the radius.
2) find the rate of change of the surface area when r = 5cm

1)

SA of sphere = 4 pi r^2
ddr = 8 pi r (im not sure why its proportional, but im 100% confident you differentiate, and then i think cause theres just on r left, its proportional - not sure of correct wording though)

2) ddr = roc = 8 pi r
let r=5
roc = 8 x pi x 5
= 40 pi

 

[gurmies]

1)

SA of sphere = 4 pi r^2
ddr = 8 pi r (im not sure why its proportional, but im 100% confident you differentiate, and then i think cause theres just on r left, its proportional - not sure of correct wording though)

2) ddr = roc = 8 pi r
let r=5
roc = 8 x pi x 5
= 40 pi

It's propotional because it has the radius in there with some ratio k, in this case 8pi