The balloon has a diameter of 23(5x+7).
The radius is half the diameter:
r=21×23(5x+7)
r=43(5x+7)
The volume of a sphere is:
V=34πr3
Substituting r=43(5x+7):
V=34π[43(5x+7)]3
V=34π×6427(5x+7)3
V=192108π(5x+7)3
V=169π(5x+7)3
Differentiating with respect to x using the chain rule:
dxdV=169π×3(5x+7)2×5
dxdV=16135π(5x+7)2
The rate of change of volume with respect to x is:
dxdV=16135π(5x+7)2