Question #7e5b1

1 Answer
Jun 5, 2017

Answer:

Here's how I would do it.

Explanation:

(a) Radius of sphere

You get the radius of the sphere from the volume of the displaced water.

#V = "30 cm"^3 – "20 cm"^3 = "10 cm"^3#

The formula for the volume #V# of a sphere is

#color(blue)(bar(ul(|color(white)(a/a) V = 4/3πr^3color(white)(a/a)|)))" "#

where #r# is the radius.

We can rearrange this formula to get

#r = root3((3V)/(4π))#

#r = root3(("3 × 10 cm"^3)/(4π)) = root3("2.39 cm"^3) = "1.3 cm"#

(b) Density of metal block

You get the density #ρ# of the metal block from its mass #m# and volume #V#.

#color(blue)(bar(ul(|color(white)(a/a)ρ = m/Vcolor(white)(a/a)|)))" "#

Assume that #m = "39 g"#.

#V = "35 cm"^3 - "30 cm"^3 = "5 cm"^3#

#ρ = m/V= "39 g"/"5 cm"^3 = "7.8 g/cm"^3#

(c) Density of wood

You apparently removed the metal sphere for this experiment.

The original volume was #"20 cm"^3#.

The metal block had a volume of #"5 cm"^3#, so

#"Volume of water + metal = 25 cm"^3#.

When you submerged the wooden block,

#"Volume of water + metal + wood = 40 cm"^3#.

∴The volume of the wooden block is

#V = "40 cm"^3 - "25 cm"^3 = "15 cm"^3#

Assume that the mass of the wood is 7.5 g. Then

#ρ = m/V = "7.5 g"/"15 cm"^3 = "0.50 g/cm"^3#