Question

A piece of copper is shaped like a sphere. The diameter of the sphere is 2.80×10¹ mm. If this sphere is placed into a graduated cylinder that has 2.50×10¹mL of water already in it, what will be the new reading on the graduated cylinder, in mL? The density of copper is 8.96g/cm³.

a) 2.50×10¹mL
b) 5.30×10¹mL
c) 2.80×10¹mL
d) 2.60×10¹mL

Answer 1

To find the new reading on the graduated cylinder after placing a copper sphere into it, calculate the volume of the sphere using its diameter, convert that volume to mL, and add it to the initial amount of water in the cylinder.

Step-by-step explanation:

To solve this, we can determine the volume of the sphere using the formula for the volume of a sphere, which is V = 4/3 * π * r3, where 'r' is the radius of the sphere. The diameter is given as 2.80 × 101 mm, which is equal to 28 mm, so the radius is 14 mm or 1.4 cm (since there are 10 mm in 1 cm). Therefore, we calculate the volume: V = 4/3 * π * (1.4 cm)3. To find the displaced water volume when the sphere is submerged, simply use the volume of the sphere. This volume is equal to the increase in the water level in the graduated cylinder. After calculating the volume of the sphere, convert the volume from cm3 to mL (since 1 cm3 = 1 mL), then add this volume to the initial water volume in the graduated cylinder (2.50 × 101 mL) to get the new reading.