Comments (8) on “What is the volume of the following rectangular prism?”

  1. A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct.

    Step-by-step explanation:

    [tex]\text{The formula of a volume of a pyraimid:}\\\\V=\dfrac{1}{3}BH\\\\B-base\ area\\H-height\\\\\text{We have}\ H=5\ \text{and}\ V=50.\ \text{Substitute and calculate thw base area:}\\\\50=\dfrac{1}{3}B(5)\qquad\text{multiply both sides by 3}\\\\150=5B\qquad\text{divide both sides by 5}\\\\30=B\to B=30\ units^2[/tex]

    [tex]\text{The formula of a volume of a prism:}\\\\V=BH\\\\B-base\ area\\H-height\\\\\text{We have}\ B=30\ \text{and}\ H=5.\ \text{Substitute:}\\\\V=(30)(5)=150\ units^3[/tex]

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  2. 1/10 units ^3

    Step-by-step explanation:

    The formula for the volume is given by

    V = Bh where B is the area of the base and h is the height

    V = 3/20 units ^2 * 2/3 units

       = 3/20 * 2/3

      = 1/10 units ^3

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  4. [tex]\bf \textit{volume of a pyramid} v=\cfrac{1}{3}bh~~ \begin{cases} b=area~of\\ \qquad its~base\\ h=height\\ \cline{1-1} v=60\\ h=5 \end{cases}\implies 60=\cfrac{1}{3}b(5)\implies 60=\cfrac{5b}{3} 180=5b\implies \cfrac{180}{5}=b\implies \boxed{36=b} [-0.35em] ~\dotfill \textit{volume of a prism} v=bh~~ \begin{cases} b=36\\ h=5 \end{cases}\implies v=(36)(5)\implies \boxed{v=180}[/tex]

    now, notice both volume equations, (1/3)bh and bh, the pyramid's is one-third of the other, meaning the prism is 3 times as large.

    so she's correct, for the prism when ba = 36 and h= 5, v = 180.

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