Question

Find the mass of $200$ steel spherical ball bearings, each of which has radius $0.7cm$, given that the density of steel is $7.95g/{cm}^3$. (Mass $=$ Volume $\times$ Density)

• A. $2.29Kg$
• B. $2.9Kg$
• C. $3.29Kg$
• D. None of these

Answer 1

The correct option is A $2.29Kg$

We have,

$200$ steel spherical balls

$r=0.7cm$

$density=7.95g/c{m}^3$

We know that the volume of the sphere

$=\frac{4}{3}\pi r^3$

So, the Volume of the $200$ steel balls

$V=200\times \frac{4}{3}\times \frac{22}{7}\times (0.7{)}^3$

$V=200\times \frac{4}{3}\times \frac{22}{7}\times 0.7\times 0.7\times 0.7$

$V=200\times \frac{4}{3}\times 22\times 0.1\times 0.49$

$V=287.467c{m}^3$

We know that

$Mass=Volume\times density$

So,

$Mass=287.467\times 7.95$

$Mass=2285.36gm$

$Mass=2.28536\approx 2.29Kg$

Hence, this is the answer.