Probem solving

Question

A balloon (in the shape of a sphere) is being inflated. The radius is increasing at a rate of 1 cm per second. Find
a function, r(t), for the radius in terms of t. Find a function, V(r), for the volume of the balloon in terms of r.
Find (V ?? r)(t).
1

Answer 1

The formula for the volume of a sphere is 4/3 * π (π is the symbol for pi) * r³.

The rate for the radius is 1cm/1s.

 

So the formula looks like: Volume = (4/3) * π * ((1cm * 1cm * 1cm)/(1s * 1s * 1s))

Simplified a little looks like: Volume = (4/3) * π * (1cm³/1s³).

Simplified more looks like: Volume = (4 * π * 1cm³)/(3 * 1s³)

So, completely simplified it looks like: Volume = (4*π*cm³)/(3*s³)

The answer is then approximately equal to (4*3.14cm³)/(s³) = 12.56cm³/3s³ = 4.19 cm³/s³.

 

The function is directly: (V=(4π)/3 cm³/s³ where s=seconds. The approximate answer is: 4.19 cm³/s³ .