A cube's volume can be calculated by multiplying its length, width, and height. What is the volume in cubic centimetres of an item with a volume of  $1.44 \mathrm{~m}^3$? The conversion factor must be multiplied by either side.

Volume Calculation

A cylindrical vessel has a radius of 7 cm and a height of 8 cm. Write a program that calculates the volume of this vessel using the following formula: volume of cylinder = 3.14 * $(radius)^2$

MURDER TO GO! writes and manufactures murder mystery parlor games that it sells to retail stores. The following is per-unit information relating to the manufacture and sale of this product:

Determine the following, showing as part of your answer the formula that you used in your computation. For example, the formula used to determine the contribution margin ratio (part a) is:

$$\text { Contribution Margin Ratio }=\frac{\text { Unit Sales Price }-\text { Variable Costs per Unit }}{\text { Unit Sales Price }}$$

a. Contribution margin ratio.

Write the correct answer.

The volume of a freshwater tank can be expressed in terms of x, y, and z. Expressed in these terms, the volume of the tank is x raised to 3y raised to (-2) z liters. Determine the volume of the tank if x = 4, y = 3, and z = 6.

Which of these values would normally be the highest?
a. tidal volume
b. inspiratory reserve volume
c. expiratory reserve volume
d. vital capacity
e. It would differ from one person to another.

The volume of a rectangular prism can be found with the formula $\mathbf{V}=\ell w h$, in which V is the volume, $\ell$ is the length, w is the width, and h is the height. Describe the effect on the volume of multiplying the height of a rectangular prism by 5.

A board foot is a unit for measuring wood. One board foot has a volume of 144 cubic inches. The Doyle log rule, given by expression $b=l\left(\frac{r-2}{2}\right)^2$, is a formula for approximating the number b of board feet in a main trunk of a Douglas fir that can be modeled by expression $V=250 r^3$ where r is the radius of the trunk at the base of the tree. Suppose you need 5000 board feet from a 20-foot Douglas fir log. What is the total volume of wood in the main trunk of a Douglas fir tree that will meet your needs?

You are given two pieces of information: (1) the volume of a lake in cubic feet and (2) the average depth of the lake in feet. You are asked to find the surface area of the lake in square feet. You should a. multiply the volume by the depth. b. divide the volume by the depth. c. divide the depth by the volume.

The ratio of the volume of Cylinder A to the volume of Cylinder B is 1:5. Cylinder A is similar to Cylinder C with a scale factor of 1:2 and Cylinder B is similar to Cylinder D with a scale factor of 1:3. What is the ratio of the volume of Cylinder C to the volume of C ylinder D ? Explain your reasoning.

Imagine a cube whose sides are expanding at a given rate (so that the volume is also increasing). Since the volume is the cube of the length of a side, is it true that the rate of change of the volume is the cube of the rate of change of the side?

A unit vector lies in the xy plane, at an angle of $160^{\circ}$ from the +x axis, with a positive y component. What is the unit vector? (It helps to draw a diagram.)

Place the figure in a coordinate plane. Label the vertices and give the coordinates of each vertex. A 5-unit by 8-unit rectangle with one vertex at (0,0).

At an instant in time the control volume and the system occupy the volume inside the pump shown, and a few diameters of the pipe at the inlet side. Sketch the system and the control volume at times $t$ and $t+\Delta t$.

Which of the following changes will accompany the loss of lung elasticity associated with aging? a. Increase in tidal volume, b. Increase in inspiratory reserve volume, c. Increase in residual volume, d. Increase in vital capacity.