Mathematics: Two similar pyramids have lateral areas 20 ft2 and 45 ft2. the volume of the smaller pyramid is 8 ft3. what is the volume of the larger pyramid?

Two similar pyramids have lateral areas 20 ft2

Ответ:

gracepiechowiak

11.01.2022

$\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\$

$\bf \cfrac{small}{large}\qquad \cfrac{\sqrt{20}}{\sqrt{45}}=\cfrac{\sqrt[3]{8}}{\sqrt[3]{v}}\implies \cfrac{2\underline{\sqrt{5}}}{3\underline{\sqrt{5}}}=\cfrac{2}{\sqrt[3]{v}}\implies \cfrac{2}{3}=\cfrac{2}{\sqrt[3]{v}}
\\\\\\
\sqrt[3]{v}=3\implies v=3^3\implies v=27$

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Ответ:

tatayanamarie5909

18.02.2020

Mathematics

sinx = cosy

Step-by-step explanation:

Hypotenuse = sqrt(4² + 3²)

= sqrt(25)

= 5

sinx = 3/5

cosy = 3/5

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Two similar pyramids have lateral areas 20 ft2 and 45 ft2. the volume of the smaller pyramid is 8 ft3. what is the volume of the larger pyramid?

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