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

Step-by-step explanation

From the question,


`M=56.3g \\ D = 6.73g/ {cm}^(3) \\ l = 12.0cm`


`D = (M)/(V)`

This implies that,


`M=V * 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


`(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 * 56.3}{{\pi \: * 12 * 6.73}}}`


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

Hence the diameter of the object is 0.94 cm