1 of 8 0-day streak

Calculate and interpret average and instantaneous rates from a model

Question 1 of 8

No calculator

The volume changes as the displayed length changes

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=4\,m,\quad H=6\,m

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

r=3\,m

Use the geometric information to select the correct model and rate

(a)1 mark

Select the correct one-variable model for the volume

V(r)=\frac{3}{2}\pi\,r^{3}

V(r)=\frac{2}{3}\pi\,r^{3}

V(r)=\frac{3}{2}\pi\,r^{2}

(b)4 marks

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

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

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)