10.7.0: Exercises
- Page ID
- 171798
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Find the volume of the right triangular prism with the two side legs of the base equal to 10 m, the hypotenuse equal to \(10\sqrt 2 \), and the height or the length, depending on your viewpoint, is equal to 15 m.
Find the surface area of the right triangular prism in the Exercise 1 with the two legs of the base equal to 10 m, and the height equal to 15 m.
Find the surface area of the right trapezoidal prism with side \({\text{a = }}5\,{\text{cm}}\), side \({\text{b = }}{\text{12}}\,{\text{cm}}\), the height is 10 cm, the slant length is 12 cm, and the length is 24 cm.
Find the volume of the trapezoidal prism in the exercise above where the base and top have the following measurements: side \(a = 5\,\text{cm}\), side \(b = 12\,\text{cm}\), the slant lengths are each \(12\,\text{cm}\), and the height of the trapezoidal base =\(10\,\text{cm}\). The height or length of the three-dimensional solid is \(24\,\text{cm}\).
Find the surface area of the octagonal prism. The base and top are regular octagons with the apothem equal to 10 m, a side length equal to 12 m, and a height of 30 m.
Find the volume for the right octagonal prism, with the apothem equal to 10 m, the side length of the base is equal to 12 m, and the height equal to 30 m.
You decide to paint the living room. You will need the surface area of the 4 walls and the ceiling. The room measures 20 ft long and 14 ft wide, and the ceiling is 8 ft high.
For the following exercises, find the surface area of each right cylinder.
\(r = 6\,\text{cm},\,h = 5\,\text{cm}\)
\(r = 9\,\text{cm},\,h = 15\,\text{cm}\)
\(r = 12.2\,\text{in},\,h = 30\,\text{in}\)
\(r = 3.4\,\text{m},\,h = 10.5\,\text{m}\)
\(d = 11.4\,\text{m},\,h = 4.4\,\text{m}\)
\(d = 20\,\text{in},\,h = 8.5\,\text{in}\)
For the following exercises, find the volume of each right cylinder to the nearest tenth.
\(r = 7\,\text{cm},\,h = 8\,\text{cm}\)
\(r = 14\,\text{cm},\,h = 19\,\text{cm}\)
\(r = 14\,\text{in},\,h = 30\,\text{in}\)
\(r = 4.9\,\text{m},\,h = 17\,\text{m}\)
\(r = 12.6\,\text{cm},\,h = 16.2\,\text{cm}\)
You have remodeled your kitchen and the exhaust pipe above the stove must pass through an overhead cabinet as shown in the figure. Find the volume of the remaining space in the cabinet.
