A cup is a measure of volume, but a gram is a measure of mass.
Depending on the density of the material you are going to have in the
cup, the weight in grams of the material will vary. For example, if you
fill the cup with lead, the cup will weigh much more than if you fill
with feathers.
This question would be similar to asking how much
does a 6 foot person weigh. It depends on the person of course. A cup of
water will weigh more than a cup of flour.
Examples:
Granulated sugar: 1 cup = 200 grams
Brown sugar: 1 cup, packed = 220 grams
Sifted white flour: 1 cup = 125 grams
White rice, uncooked: 1 cup = 185 grams
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