How many cubic centimeters (cm^3) are in a box that measures 2.20 in. by 4.00 in. by 6.00 in.?

Question

How many cubic centimeters ([latex]cm^3[/latex]) are in a box that measures 2.20 in. by 4.00 in. by 6.00 in.?

Accepted Answer

First we need to determine the volume of the box in cubic inches [latex](in.^3)[/latex] by multiplying the length [latex] imes[/latex] width [latex] imes[/latex] height:

(2.20 in.)(4.00 in.)(6.00 in.) = 52.8 [latex]in.^3[/latex]

Now we convert [latex]in.^3 [/latex] to [latex]cm^3[/latex] by using the inches and centimeters relationship (1 in. = 2.54 cm) three times:

Solution map: [latex]( in.→cm)^3[/latex]

[latex]\cancel{in.^3} imes \frac{cm}{\cancel{in.}} imes \frac{cm}{\cancel{in.}} imes \frac{cm}{\cancel{in.}}= cm^3[/latex]

[latex](52.8 \cancel{in.^3}) (\frac{2.54 cm}{1 \cancel {in}}) (\frac{2.54 cm}{1 \cancel {in}}) (\frac{2.54 cm}{1 \cancel {in}}) =865 cm^3[/latex]

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