Find the volume of a cuboid. Three different walls of the cuboid have areas: 96,...

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CrushMo2 @CrushMo2

September 2022 1 1 Report

Find the volume of a cuboid. Three different
walls of the cuboid have areas: 96,48,32

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Blevins

• Question:

Find the volume of a cuboid. Three different

walls of the cuboid have areas: 96,48,32

______________________________

• Solution:

Use Formula: V = a × b × c

The cuboid walls are rectangles or squares, so the formula for an area of each wall is P = a × b. To calculate the length of the sides solve the following system of equations:

$\begin{cases}a \times b = 96 \\ a \times c = 48 \\ b \times c = 32 \end{cases}$

$\begin{cases}a = \frac{96}{b} \\ a \times c = 48 \\ b \times c = 32 \end{cases}$

$\begin{cases}\frac{96}{b} \times c = 48 \\ b \times c = 32 \end{cases}$

$\begin{cases}c = 48 \times \frac{b}{96} \\ b \times c = 32\end{cases}$

$\begin{cases}b \times (48 \times \frac{b}{96}) = 32 \\ \frac{48b^2}{96} = 32 \end{cases}$

$\begin{cases}\frac{48b²}{96} = 32 \\ 48b² = 3072 \\ b = \sqrt{\frac{3072}{48}} = 8\end{cases}$

$c = 48 \times \frac{b}{96} = 48 \times \frac{8}{96} = 4$

$a = \frac{96}{b} = \frac{96}{8} = 12$

$\boxed{\underline{V = a \times b \times c = 12 \times 8 \times 4 = \underline{{\boxed{\red{384}}}}}}$

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