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A piece of wood has a mass of $m_1$ grams and a volume of $V_1$ cubic centimeters. A second piece of wood has the same density $\rho$ and a volume of $V_2$ . What is the mass, in grams, of the second piece of wood?

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. A piece of wood has a mass of

m_1

grams and a volume of

V_1

cubic centimeters. A second piece of wood has the same density

\rho

and a volume of

V_2

. What is the mass, in grams, of the second piece of wood?

Identify values and formula: Identify the known values and the formula for density. Density is mass divided by volume. The first piece of wood has a known mass $m_1$ and volume $V_1$ , and the second piece of wood has an unknown mass $m_2$ and a known volume $V_2$ . The density $D$ for both pieces of wood is the same. Density formula: $D = \frac{m_1}{V_1} = \frac{m_2}{V_2}$
Calculate first piece density: Calculate the density of the first piece of wood using its mass and volume. $\newline$ Since the mass and volume of the first piece of wood are not given numerically, we cannot calculate the actual density. However, we can express the density in terms of the given variables. $\newline$ Let's denote the mass of the first piece of wood as $m_1$ grams and its volume as $V_1$ cubic centimeters. $\newline$ Density of the first piece of wood: $D = \frac{m_1}{V_1}$
Express second piece mass: Express the mass of the second piece of wood in terms of its volume and the density. $\newline$ Using the density formula, we can express the mass of the second piece of wood $m_2$ as follows: $\newline$ $m_2 = D \times V_2$ $\newline$ Since $D = \frac{m_1}{V_1}$ , we can substitute this into the equation for $m_2$ : $\newline$ $m_2 = \left(\frac{m_1}{V_1}\right) \times V_2$
Calculate second piece mass: Since the problem does not provide numerical values for $m_1$ , $V_1$ , or $V_2$ , we cannot calculate the exact mass of the second piece of wood. We need these values to proceed with the calculation. $\newline$ Without numerical values, we cannot provide a numerical answer for the mass of the second piece of wood ( $m_2$ ).

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