# composite function involving word problem

• Dec 8th 2009, 05:29 PM
extraordinarymachine
composite function involving word problem

A spherical hailstone grows in a cloud. The hailstone maintains a spherical shape while its radius increases at a rate of 0.2 mm/min.

a) Express the radius, r, in millimeters, of the hailstone, as a function of the time, t, in minutes.

i came up with the answer,
r(t) = 0.2t
but i'm not sure if its right

b) Express the volume, V, in cubic millimeters, of the hailstone, in terms of r.

i got,
V(r) = $\displaystyle \frac{4}{3}{\pi}(0.2t)^3$

c) Determine (Vor)(t)

Vor(t) = $\displaystyle \frac{4}{3}{\pi}(0.2t)^3$
not sure if thats right either?

d) What is the volume of the hailstone 1 h after it begins to form?
• Dec 8th 2009, 05:53 PM
skeeter
Quote:

Originally Posted by extraordinarymachine

A spherical hailstone grows in a cloud. The hailstone maintains a spherical shape while its radius increases at a rate of 0.2 mm/min.

a) Express the radius, r, in millimeters, of the hailstone, as a function of the time, t, in minutes.

i came up with the answer,
r(t) = 0.2t
but i'm not sure if its right

correct

b) Express the volume, V, in cubic millimeters, of the hailstone, in terms of r.

i got,
V(r) = $\displaystyle \frac{4}{3}{\pi}(0.2t)^3$

you went one step too fast ...

$\displaystyle \textcolor{red}{V(r) = \frac{4}{3}\pi r^3}$

c) Determine (Vor)(t)

Vor(t) = $\displaystyle \frac{4}{3}{\pi}(0.2t)^3$
not sure if thats right either?

correct

d) What is the volume of the hailstone 1 h after it begins to form?

... sub in 60 for t and calculate the volume.

...
• Dec 8th 2009, 05:59 PM
extraordinarymachine
thanks!

and i did sub in 60 to calculate the volume, and i got 7238? is this correct?