# math

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

dv/dt = 4π * 25 * 1 = 100π cm^3/s

posted by Steve

## Similar Questions

1. ### 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? (VOLUME SPHERE FORMULA 4/3 pi r^3)
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
3. ### 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
4. ### 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.?
5. ### 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
6. ### 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
7. ### 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
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. ### math

Air is pumped into a balloon such that its volume increases at the rate of 75cm^3 per second. It is assumed that the balloon is spherical all the time. Find in term of pi the rate at which the radius of the balloon is increasing
10. ### Calculus

suppose that a tumor on a person's body is spherical in shape. if the radius of the tumor is 0.5cm the radius is increasing at the rate of 0.001cm per day. what is the rate of increasing volume of that tumor at that time?

More Similar Questions