A student using a 100mL graduated cylinder that contained 50.00mL of water. Th volume of the water increased to 57.50mL. The density of the object was 7.85 g/cm^2. How many grams did the metal object weigh?
mass object = volume x density
volume = 57.50-50.00 = ?
density = given.
Solve for mass object.
isn't the density given in g/cm^2 though? and the mass is mL. It seems like there are 2 different units here. They also want the answer in grams.
so m= d x v
7.50mL x 7.85 g/cm^2= 58.9 (what unit mL or g.cm^2?)
1 mL = 1 cm^3 = 1 cubic centimeter = 1 cc.
7.50 cc x 7.85 g/cc = 58.9 grams. Note that cc in numerator cancels with cc in the denominator.
To find the weight of the metal object, we first need to calculate the change in volume of water in the graduated cylinder and then use the density to calculate the weight. Here's how to do it step by step:
1. Calculate the change in volume of the water: Subtract the initial volume from the final volume.
Change in volume = Final volume - Initial volume
Change in volume = 57.50 mL - 50.00 mL
Change in volume = 7.50 mL
2. Convert the change in volume to cm^3, as the density is given in grams per cm^3. Since 1 mL is equal to 1 cm^3, there is no need for conversion in this case.
Change in volume = 7.50 cm^3
3. Use the formula density = mass / volume to calculate the mass of the metal object.
Rearrange the formula to find mass:
Mass = Density x Volume
Mass = 7.85 g/cm^3 x 7.50 cm^3
4. Calculate the mass of the metal object using the values obtained in the previous steps:
Mass = 58.875 g
Therefore, the metal object weighs approximately 58.875 grams.