Mathematics: Arectangular pyramid has a height of 5 units and a volume of 60 units^3. shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. which statement explains whether shannon is correct? a.a rectangular prism in which ba = 36 and h = 5 has a volume of 180 units^3; therefore, shannon is correct. b.a rectangular prism in which ba = 12 and h = 5 has a volume of 180 units^3; therefore, shannon is correct. c.a rectangular

Arectangular pyramid has a height of 5 units and

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31.07.2019

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