We are given the formula for the volume, V, as ​\( V \)​=​\( l \)​ x ​\( w \)​ x ​\( h \)​, where l is the length, w is the width, and his the height of the prism. Substituting our values into thevolume formula, we get:
V=152.84 cm x 48.67 cm x 60.38 cm=449,150.0827 cm³
So, to the nearest cubic centimeter, the volume is449, 150cm³.
Be careful about rounding the dimensions of the box to thenearest centimeter first before taking their product to get thevolume of the box. Rounding this way can produces largererrors for the volume of the box versus rounding the volumeafter taking the product of the dimensions.
If we rounded the dimensions to the nearest whole number first, we get:
V=153 x 49 x 60=449,820
This is answer choice A, but as you can see, the correct answer choice of 449,150 cm³ is much closer to the actual volume of 449,150.0827 cm³. This is because of our choice to round the volume after the product of the dimensions versus rounding the dimensions first to determine the volume. Rounding before taking the product would be considered an estimate.