How many cubic inches are there in 3.25 yd³? Express the volume in cubic inches to three significant figures.
The Correct Answer and Explanation is:
To solve this, we need to convert 3.25 cubic yards (yd³) to cubic inches (in³).
Step-by-Step Conversion:
1 yard = 36 inches
So,
1 cubic yard (yd³) = 36336^3 cubic inches
= 36×36×36=46,65636 \times 36 \times 36 = 46,656 in³
Now multiply this by 3.25: 3.25×46,656=151,632 in33.25 \times 46,656 = 151,632 \text{ in}^3
Final Answer (to three significant figures):
1.52×105 in3\boxed{1.52 \times 10^5 \text{ in}^3}
Explanation
To convert a volume given in cubic yards to cubic inches, it’s important to remember that we’re dealing with a cubic conversion, not a simple linear conversion. This means the unit conversion factor must be raised to the power of three. Since 1 yard equals 36 inches, one cubic yard is 363=46,65636^3 = 46,656 cubic inches.
In this problem, we’re given a volume of 3.25 cubic yards. To find the equivalent in cubic inches, multiply 3.25 by the number of cubic inches in one cubic yard: 3.25 yd3×46,656 in3/yd3=151,632 in33.25 \text{ yd}^3 \times 46,656 \text{ in}^3/\text{yd}^3 = 151,632 \text{ in}^3
This gives us the raw answer, but the question specifically asks for the volume to be expressed to three significant figures. The number 151,632 has six significant figures. To round it to three significant figures, we identify the first three digits (1, 5, and 2), then round appropriately: 151,632≈1.52×105 in3151,632 \approx 1.52 \times 10^5 \text{ in}^3
This scientific notation form is commonly used in science and engineering for clarity and precision, especially with large or small numbers.
In summary, unit conversion involving cubic measurements must always cube the linear conversion factor, and the result should be expressed in the correct number of significant figures as required. The final volume of 3.25 yd³ is 1.52 × 10⁵ in³ to three significant figures.
