Convert 7.6 $cm ^3$ to $m ^3$
Answer (2)
To convert 7.6 cubic centimeters (cm³) to cubic meters (m³), cube the conversion of 1 m = 100 cm, resulting in 1 c m 3 = 1 0 − 6 m 3 . Thus, multiplying 7.6 cm³ by 1 0 − 6 gives 7.6 × 1 0 − 6 m³. Hence, the final answer is 7.6 × 1 0 − 6 m³.
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Recognize the need to convert cubic centimeters ( c m 3 ) to cubic meters ( m 3 ).
Recall the relationship 1 m = 100 c m and cube it to find the conversion factor for volume: 1 c m 3 = ( 0.01 m ) 3 = 1 0 − 6 m 3 .
Multiply the given volume by the conversion factor: 7.6 c m 3 × 1 0 − 6 c m 3 m 3 .
State the final answer in cubic meters: 7.6 × 1 0 − 6 m 3 .
Explanation
Problem Analysis We are asked to convert a volume from cubic centimeters ( c m 3 ) to cubic meters ( m 3 ). The given volume is 7.6 c m 3 . We need to find the equivalent volume in m 3 .
Basic Conversion First, we need to recall the relationship between centimeters and meters. We know that 1 meter (m) is equal to 100 centimeters (cm). 1 m = 100 c m
Cubic Conversion Factor To convert cubic centimeters to cubic meters, we need to cube the conversion factor. Since 1 c m = 0.01 m , then: 1 c m 3 = ( 0.01 m ) 3 = 0.0 1 3 m 3 = 0.000001 m 3 = 1 0 − 6 m 3
Applying the Conversion Now, we multiply the given volume in c m 3 by the conversion factor to get the volume in m 3 :
7.6 c m 3 × 1 c m 3 1 0 − 6 m 3 = 7.6 × 1 0 − 6 m 3
Final Answer Therefore, 7.6 c m 3 is equal to 7.6 × 1 0 − 6 m 3 .
Examples
Imagine you are designing a miniature garden in a terrarium and need to calculate the volume of soil required. If you measure the volume in cubic centimeters but need to order soil in cubic meters, this conversion becomes essential. Knowing how to convert between these units allows you to accurately determine the amount of material needed, ensuring your miniature garden thrives without overfilling or underfilling the space.
