Pregunta
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2. Find the volume of a cube with \( 11 / 4 \)-inch sides.

Ask by Dunn Schwartz. in the United States
Mar 18,2025

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The volume of the cube is \( \frac{1331}{64} \) cubic inches, which is approximately 20.796875 cubic inches.

Solución

To find the volume of a cube, we use the formula: \[ V = s^3 \] where \( V \) is the volume and \( s \) is the length of a side of the cube. Given that the side length of the cube is \( \frac{11}{4} \) inches, we can substitute this value into the formula to find the volume: \[ V = \left(\frac{11}{4}\right)^3 \] Now, we can calculate the volume of the cube. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{11}{4}\right)^{3}\) - step1: Use the properties of exponents: \(\frac{11^{3}}{4^{3}}\) - step2: Evaluate the power: \(\frac{1331}{4^{3}}\) - step3: Evaluate the power: \(\frac{1331}{64}\) The volume of the cube with \( \frac{11}{4} \)-inch sides is \( \frac{1331}{64} \) cubic inches, which is equivalent to \( 20\frac{51}{64} \) cubic inches or approximately 20.796875 cubic inches.

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Extra Insights

To find the volume of a cube, you simply raise the length of one side to the third power (multiply it by itself three times). So for a cube with sides of \( \frac{11}{4} \) inches, the volume would be: \[ \text{Volume} = \left( \frac{11}{4} \right)^3 = \frac{11^3}{4^3} = \frac{1331}{64} \text{ cubic inches}. \] That gives you a volume of approximately \( 20.828125 \) cubic inches! Measuring your cube's volume can come in handy in many real-world situations. For example, if you're packing boxes for a move or calculating how much space you'll need for storage, knowing the volume helps you make better decisions about how many items will fit—or if you need a bigger box! When calculating the volume, a common mistake is forgetting to cube the side length correctly, especially when working with fractions. Always double-check your math: \( \frac{11}{4} \) needs to be multiplied three times! Additionally, it’s super helpful to convert fractions to decimals before multiplying if that feels easier.

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