Question

A spherical ball of lead has a diameter of 2.5 cm . What is the mass of the sphere if lead has a density of 11.34 g/cm3? (The volume of a sphere is (43)πr3 where r is the radius.)

Answer 1

Answer : The mass of sphere is 92.727 grams.

Explanation :

To calculate the volume of sphere, we use the formula:

$V=\frac{4}{3}\pi r^3$ .....(1)

where,

r = radius of sphere

Given :

Diameter of sphere = 2.5 cm

Radius of sphere = $\frac{Diameter}{2}=\frac{2.5cm}{2}=1.25cm$

Now put all the given values in the above formula (1), we get:

$V=\frac{4}{3}\times 3.14\times (1.25cm)^3$

$V=8.177cm^3$

To calculate mass of a substance, we use the equation:

$Density=\frac{Mass}{Volume}$ .....(2)

Putting values in above equation (2), we get:

$11.34g/cm^3=\frac{Mass}{8.177cm^3}$

$Mass=92.727g$

Hence, the mass of sphere is 92.727 grams.

Answer 2

Mass =  volume  x   density

volume = πr²
    since Diameter = 2.5 cm
    then   radius = 1.25cm

∴ volume  =  π  x  (1.25cm)³
                 ≈  6.1359 cm³

Thus mass  =  6.1359 cm³  x  11.34  g / cm³
                    =  69.58 g