Which statement is true about the volume of the water displaced by the golf ball? A It is equal to the volume of the golf ball. B It is greater than the volume of the golf ball. C It is less than the volume of the golf ball. D The volume depends on the density of the golf ball.

A recent study showed that the systolic blood pressure of high school students ages 14-17 is normally distributed with a mean of 120 and a standard deviation of 12. Suppose a high school has 800 students. About what percent of the students have blood pressure below 108?

(Volume of a tetrahedron) A tetrahedron is a pyramid with a triangular base and three other triangular faces. It has four vertices and six edges. Like any pyramid or cone, its volume is equal to $\dfrac{1}{3}Ah$, where $A$ is the area of the base and $h$ is the height measured perpendicular to the base. If $\mathbf { u } , \mathbf { v }$, and $\mathbf { w }$ are vectors coinciding with the three edges of a tetrahedron that meet at one vertex, show that the tetrahedron has volume given by

$$\text { Volume } = \dfrac { 1 } { 6 } | \mathbf { u } \bullet ( \mathbf { v } \mathbf { \times} \mathbf { w } ) | = \dfrac { 1 } { 6 } | \left| \begin{array} { c c c } { u _ { 1 } } & { u _ { 2 } } & { u _ { 3 } } \\ { v _ { 1 } } & { v _ { 2 } } & { v _ { 3 } } \\ { w _ { 1 } } & { w _ { 2 } } & { w _ { 3 } } \end{array} \right| |$$

Thus, the volume of a tetrahedron spanned by three vectors is one-sixth of the volume of the parallelepiped spanned by the same vectors.

Copy and complete the table below. Then tell whether the table shows a linear relationship.

$$\begin{array}{|c|c|} \hline {\text { Volume of a Cube }} \\ \hline \text { Side Length } & \text { Volume } \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline 4 & \\ \hline \end{array}$$

A vitamin is shaped like a cylinder with congruent hemispheres on either end. If the volume of the vitamin is $22.5 \pi$ cubic millimeters, and the height of the cylindrical part is 8 millimeters, what is the radius of the vitamin?

The table shows the relationship between the temperature of a sample of helium and its volume.

$$\begin{array}{|r|c|c|c|c|c|} \hline Temperature \left({ }^{\circ} \mathrm{C}\right) & 0 & 25 & 50 & 75 & 100 \\ \hline Volume \left(\mathrm{in}^3\right) & 30 & 32.7 & 35.4 & 38.1 & 40.8 \\ \hline \end{array}$$

(a) Make a scatterplot of the data.

(b) Write a formula for a function $f$ that receives the temperature $x$ as input and outputs the volume $y$ of the helium.

$(c)$ Find the volume when the temperature is $65^{\circ} \mathrm{C}$.

(d) Find the temperature if the volume is $25$ cubic inches. Did your answer involve interpolation or extrapolation? Do you believe that your answer is accurate?

Set

$$f(x)=\left\{\begin{aligned} \sqrt{3} x, & 0 \leq x<1 \\ \sqrt{4-x^2}, & 1 \leq x \leq 2, \end{aligned}\right.$$

and let $\Omega$ be the region between the graph of $f$ and the $x$-axis.
Revolve $\Omega$ about the line $y=-1$.
(a ) Express the volume of the resulting solid as an integral in $x$.
(b ) Express the volume of the resulting solid as an integral in $y$.

Solve previous problem, but assume the steam pressure in the cylinder starts at $1000\ \mathrm{kPa}$, dropping linearly with volume to reach $100\ \mathrm{kPa}$ at the end of the process.

Complete the table.

$$\begin{array}{|c|c|c|c|} \hline l& w & h &\text{Volume}\\ \hline ?&8 & 10 & 160\\ \hline \end{array}$$

Find the volume of cone. Round to the nearest tenth.

$$\begin{array} { l } { \text { height: } 24 \text { centimeters } } \\ { \text { diameter: } 8 \text { centimeters. } } \end{array}$$

Calculate the volume of the following prisms and describe your procedure. At the end, compare your results with those of your closest partner. In case of different results, comment on the procedures that were applied.

The arterial blood pressure of an individual in a state of relaxation is given by

$$P(t)=100+20 \sin 6 t$$

where P(t) is measured in mm of mercury (Hg) and t is the time in seconds.

Show that the individual's systolic pressure (maximum blood pressure) is 120 and his diastolic pressure (minimum blood pressure) is 80 .

Compare and contrast the formulas for the volume of a pyramid and the volume of a cone.

A gas with a volume of 4.0 L is contained in a closed container. Indicate the changes in pressure when the volume undergoes the following changes at constant temperature and amount of gas:

a. The volume is compressed to 2.0 L.

b. The volume expands to 12 L.

c. The volume is compressed to 0.40 L.