1 of 8 0-day streak

Calculate and interpret average and instantaneous rates from a model

Question 1 of 8

No calculator

The following geometric data describes the changing volume

A family of similar right circular cylinders is described by radius r and height h. A reference cylinder has radius R m and height H m

R=5\,m,\quad H=8\,m

\frac{h}{r}=\frac{H}{R}

r=3\,m

Select the correct one-variable volume model, then find the rate at the stated input

(a)1 mark

Select the correct one-variable model for the volume

V(r)=\frac{8}{5}\pi\,r^{3}

V(r)=\frac{5}{8}\pi\,r^{3}

V(r)=\frac{8}{5}\pi\,r^{2}

(b)4 marks

Complete the coefficient and power entries for the model and its derivative

Coefficient of pi in the derivative Coefficient of pi in the model Power in the derivative Power in the model

Enter the coefficient of pi in the derivative at the stated input

V'(3)=k\pi

Coefficient of pi in rate (cubic metres per metre)