Question

Density of ZrC is 6.73g/cm. A cylinder of this material has a mass of 56.3 and a length of 12.0. What is the diameter of this object?

Answer 1

ANSWER:
0.94 cm

EXPLANATION

From the question,

$M=56.3g \\ D = 6.73g/ {cm}^{3} \\ l = 12.0cm$

$D = \frac{M}{V}$

This implies that,

$M=V \times D.......1$

But volume is given by the relation;

$V = \frac{\pi {d}^{2} l}{4}.......2$

Substituting equation 2 into equataion 1 and making d the subject.

$M= \frac{\pi {d}^{2} l D}{4}$

Multiplying both side of the equation by

$\frac{4}{\pi \: lD}$

gives;

${d}^{2} = \frac{4M}{{\pi \: lD}}$

square root both sides gives;

$d = \sqrt{\frac{4M}{{\pi \: lD}}} ....3$

substituting the values of M,V,D and l into equation 4 to get the value for d

$d = \sqrt{\frac{4 \times 56.3}{{\pi \: \times 12 \times 6.73}}}$

$d = 0.94 \: cm \: to \: 2d.p$

Hence the diameter of the object is 0.94 cm