Question

A spherical block of metal weighs $12$ pounds. What is the weight, in pounds, of another block of the same metal if its radius is $3$ times the radius of the $12-$pound block?

• A. $324$
• B. $15$
• C. $36$
• D. $108$

Answer 1

Answer: (A)

$324$

The weight $W$ of an object of mass $M$ is given by:

$W=Mg$, where $g$ is constant.

The mass $M$ of an object of volume $V$ is given by:

$M=dV$ , where $d$ is the density.

The weight $W$ of a spherical block of density $d$ and radius $r$ is given by:

$W=V\left(dg\right)=\frac{4}{3}\times \pi \times r^3\times \left(dg\right)$

The weight $W$ of a spherical block of density $d$ and radius $3r$ is given by:

$W=V\left(dg\right)=\frac{4}{3}\pi \times (3r{)}^3\times \left(dg\right)=27w=27\left(12\right)=324$ pounds.

Hence, the weight of another block of the same metal is $324$ pounds.