9.3.0: Exercises
- Page ID
- 171747
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)For the following exercises, determine the most reasonable value for each volume.
Fish tank:
71,120 km3, 71,120 m3, 71,120 cm3, or 71,120 mm3
Juice box:
125,000 L, 125 L, 125,000 mL, or 125 mL
Box of cereal:
2,700 km3, 2,700 m3, 2,700 cm3, or 2,700 mm3
Water bottle:
5 L, 0.5 L, 5 mL, or 0.5 mL
Shoe box:
3,600 km3, 3.6 m3, 3,600 cm3, or 3,600 mm3
Swimming pool:
45 L, 45,000 L, 45 mL, or 45,000 mL
For the following exercises, convert the given volume to the units shown.
38,861 mm3 = __________ cm3
13 dm3 = __________ mL
874 cm3 = __________ mm3
4 m3 = __________ cm3
0.00003 m3 = _________ mm3
57,500 mm3 = _______ L
0.007 m3 = __________ L
8,600 cm3 = _________ m3
45.65 m3 = _______ cm3
0.06 m3 = __________ dm3
0.081 m3 = _________ mL
3,884,000 mm3 = _______ m3
For the following exercises, determine the volume of objects with the dimensions shown.
\(30\,{\text{cm}} \times 20\,{\text{m}} \times 10\,{\text{cm}}\)
\(V =\) ________ L
\(17\,{\text{mm}} \times 3\,{\text{cm}} \times 2.5\,{\text{cm}}\)
\(V =\) ________ mL
\(3.4\,{\text{m}} \times 2.5\,{\text{m}} \times 10\,{\text{m}}\)
\(V =\) ________ m3
\(325\,{\text{mm}} \times 20\,{\text{cm}} \times 0.05\,{\text{m}}\)
\(V =\) ________ cm3
\(3.7\,{\text{m}} \times 4\,{\text{m}} \times 5.5\,{\text{m}}\)
\(V =\) ________ m3
\(18\,{\text{dm}} \times 0.8\,{\text{m}} \times 150\,{\text{cm}}\)
\(V =\) ________ L
\(15\,{\text{cm}} \times 400\,{\text{mm}} \times 3\,{\text{dm}}\)
\(V =\) ________ mL
\(3.5\,{\text{cm}} \times 200\,{\text{mm}} \times 0.7\,{\text{dm}}\)
\(V =\) ________ cm3
\(35\,{\text{m}} \times 1.2\,{\text{m}} \times 0.007\,{\text{km}}\)
\(V =\) ________ m3
A box has dimensions of \(20\,{\text{cm}} \times 15\,{\text{cm}} \times 30\,{\text{cm}}\). The box currently holds 1,250 cm3 of rice. How many cubic centimeters of rice are needed to completely fill the box?
The dimensions of a medium storage unit are \(4\,{\text{m}} \times 4\,{\text{m}} \times 8\,{\text{m}}\). What is the volume of a small storage area with dimensions half the size of the medium unit?
How much liquid, in liters, can a container with dimensions of \(40\,{\text{cm}} \times 20\,{\text{cm}} \times 120\,{\text{cm}}\) hold?
What is the volume of the rectangular prism that is shown?
A box is 15 centimeters long and 5 centimeters wide. The volume of the box is 225 cm3. What is the height of the box?
Kareem mixed two cartons of orange juice, three 2-liter bottles of soda water and six cans of cocktail fruits to make a fruit punch for a party. The cartons of orange juice and cans of cocktail fruits each have a volume of 500 cm3. How much punch, in liters, did Kareem make?
A holding tank has dimensions of \(16\,{\text{m}} \times 8\,{\text{m}} \times 8\,{\text{m}}\). If the tank is half-full, how more liters of liquid can the tank hold?
A large plastic storage bin has dimensions of \(16\,{\text{cm}} \times 16\,{\text{cm}} \times 16\,{\text{cm}}\). A medium bin’s dimensions are half the size of the large bin. A small bin’s dimensions are the size of the medium bin. If the storage bins come in a set of 3—small, medium, and large—what is the total volume of the storage bin set in cubic centimeters?
A soft serve ice cream machine holds a 19.2 liter bag of ice cream mix. If the average serving size of an ice cream cone is 120 mL, how many cones can be made from each bag of mix?
A shipping carton has dimensions of \(0.5\,{\text{m}} \times 0.5\,{\text{m}} \times 0.5\,{\text{m}}\). How many boxes with dimensions of \(50\,{\text{mm}} \times 50\,{\text{mm}} \times 50\,{\text{mm}}\) will fit in the shipping carton?
A recipe for chili makes 3.5 liters of chili. If a restaurant serves chili in 250 mL bowls, how many bowls of chili can they serve?
A contractor is building an in-ground pool. They excavate a pit that measures \(12\,{\text{m}} \times 9\,{\text{m}} \times 2.5\,{\text{m}}\). The dirt is being taken away in a truck that holds 30 m3. How many trips will the truck have to make to cart away all of the dirt?
A juice dispenser measures \(30\,{\text{cm}} \times 30\,{\text{cm}} \times 30\,{\text{cm}}\). How many 375 mL servings will a full dispenser serve?