To study fluctuations in leaf water potential, samples of wood were taken from 22 trees and cut in the shape of a cube. The length of the edge of one of these cubes is 3.000 centimeters. This cube has a density of 0.250 grams per cubic centimeter. What is the mass of this cube, in grams?

To study fluctuations in leaf water potential, samples of wood were taken from 22 trees... | SAT Ratios, rates, proportional relationships, and units Practice

Answer: $6.75$

Explanation:1. Recall the formulas for the volume of a cube and the relationship between density, mass, and volume: Volume of a cube (V) with edge length (s): $V = s^3$ Density ( $\rho$ ): $\rho = \dfrac{\text{mass (m)}}{\text{volume (V)}}$ Therefore, mass (m): $m = \rho \times V$

Calculate the volume of the cube: Edge length $s = 3.000$ centimeters. $V = (3.000 \text{ cm})^3$ $V = 3^3 \text{ cm}^3$ $V = 27 \text{ cm}^3$ (or $27.000 \text{ cm}^3$ )
Use the density and volume to find the mass: Density $\rho = 0.250$ grams per cubic centimeter ( $\text{g/cm}^3$ ). Mass $m = \rho \times V$ $m = (0.250 \text{ g/cm}^3) \times (27 \text{ cm}^3)$ $m = 0.250 \times 27 \text{ g}$
Perform the multiplication: $0.250 \times 27 = \dfrac{1}{4} \times 27 = \dfrac{27}{4}$ $\dfrac{27}{4} = 6.75$ So, $m = 6.75$ grams.

Conclusion:The mass of this cube is $6.75$ grams.

Question Bank

Question Bank

SAT Ratios, rates, proportional relationships, and units practice question

Explanation