Question

If a solid cone-shaped crystal paper-weight of density $3.1g/{cm}^3$ has height of $5$ cm and base diameter that is $20\%$ larger than the height, the approximate mass (round to nearest gram) of the paperweight, is

• A. $146$
• B. $184$
• C. $164$
• D. $144$

Answer 1

The correct option is A $146$

The height of the cone shaped crystal is $h=5$ cm.

Its base diameter $=5+20\%$ of $5=6$ cm.

Then, its radius $r=\frac{d}{2}=\frac{6}{2}$ cm.

Its volume = $\frac{1}{3}\times \pi r^{2}h$

$=\frac{1}{3}\times \pi \times {\left(\frac{6}{2}\right)}^2\times 5$

$=47.12cc$.

Since the density is given to be $3.1$ g/cc,

then the mass becomes volume $\times$ density

$=47.12\times 3.1$

$=146.072$ gram.

Then, to nearest gram, the mass is $146$ gram.

Hence, option $A$ is correct.