# math

posted by Prince

An elastic spherical ballon is being blown up so that the radius is increasing at a rate of 1cm/sec. Calculate the rate at which the volume of the ballon is increasing when the radius is 5cm

1. Steve

v = 4π/3 r^3
dv/dt = 4π r^2 dr/dt
when r=5,

dv/dt = 4π * 25 * 1 = 100π cm^3/s

## Similar Questions

1. ### calculus

This one is tough. "A ballon in the shape of a cylinder with hemispherical ends of the same radius as that of the cylinder is shown. The ballon is being inflated at the rate of 261pi cubic centimeters per minute. At the instant the …
2. ### math

This one is kinda hard. "A ballon in the shape of a cylinder with hemispherical ends of the same radius as that of the cylinder is shown. The ballon is being inflated at the rate of 261pi cubic centimeters per minute. At the instant …
3. ### math

RATES OF CHANGE QUESTION A spherical balloon is being blown up so that its volume is increasing by 0.6 m^3 s^-1. Find the rate at which the radius is increasing when the radius is 0.1 m. So what I did was that I determined dV/dt =0.6 …
4. ### Calculus

a spherical ballon is being inflated at a constant rate of 25 cm^3/sec. At what rate in cm/sec is the radius of the ballon changing when the radius of the ballon is 2 cm?
5. ### Math

A spherical balloon is being inflated so that its volume is increasing at the rate of 200 cm3/min. At what rate is the radius increasing when the radius is 15 cm.
6. ### calculus

a splenical ballon is being inflated @ 10 cubic inches per secound. how fast is the radius of the ballon increasing when the surface area of the ballon is 2 pi square inches( answer to 4 decimal places)?
7. ### Math

A spherical balloon is inflated with helium at the rate of 100pi ft ^3/min. How fast is the ballon's radius increasing at the instant the radius is 5ft.?
8. ### Calculus

If the volume of a spherical ballon is increasing at 4 pi m^3/ min when its radius is 2m, how fast is its surface are increasing at the same time
9. ### maths

a spherical ballon is being inflated at the rate of 10 cu in/sec.find the rate of change of area when ballon has a radius of 6 inch. (a)3.33 in2/sec (b)3.67 in2/sec (c)3.11 in2/sec (d)none of these
10. ### math

a spherical ballon is inflated with gas at the rate 20cm^3 min. how fast is the radius of the ballon changing at the instant when the radius is 2cm

More Similar Questions