Final answer:
To convert 2.60 cubic foot (ft³) to cubic centimeters (cm³), convert the cubic feet to cubic inches first, and then convert those cubic inches to cubic cm. The final result is approximately 73597.624 cm³.
Step-by-step explanation:
To find the number of cubic centimeters (cm³) in 2.60 cubic feet (ft³), we need to use conversion factors and dimensional analysis. First, it's essential to know the conversion between different units involved; the conversion factors we know are that 1 inch equals 2.54cm and 1 foot equals 12 inches.
However, those are linear measurements, and here we are dealing with cubic measurements. Both these amounts should be cubed when converting from cubic feet to cubic cm. Therefore, (1ft)³ is (12in)³, and equivalently, (2.54cm)³. The total is cubic inches to cubic cm.
Here is a step-by-step solution:
- Start with the value you are given, 2.60 ft³.
- First convert from cubic feet to cubic inches. We know that 1 ft is equal to 12 inches. But, since we are dealing with cubic feet and cubic inches, we need to cube the conversion factor. Therefore, 1 ft³ is equal to (12 in)³ or 1728 in³. So, 2.60 ft³ can be converted to cubic inches by multiplying 2.60 ft³ by 1728 in³/ft³. This gives us 4488.8 in³.
- Next, convert from cubic inches to cubic cm. We know that 1 inch is equal to 2.54 cm. Again, since we are dealing with cubic inches and cubic cm, we need to cube this conversion factor. So, 1 in³ is equal to (2.54 cm)³ or 16.387 cm³. So, 4488.8 in³ can be converted to cubic cm by multiplying 4488.8 in³ by 16.387 cm³/in³. This gives us 73597.624 cm³.
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