Question

Find the weight of a solid cone whose base is of diameter $42cm$ and vertical height $20cm$, supposing that the material of which it is made weights $5$ grams per cubic centimetre.

• A. $46.2kg$
• B. $43.2kg$
• C. $44.2kg$
• D. $42.2kg$

Answer 1

Answer: (A)

Given that,
The diameter of the base of a cone is $42cm$ and its height is $20cm$.

Also, $1c{m}^3$ of the material which the cone is made of weights $5$ grams.

To find out,

The weight of the cone.

We know that, volume of a cone $=\frac{1}{3}\pi r^{2}h$

Here, $r=\frac{42}{2}=21cm$ and $h=20cm$

Hence, volume $=\frac{1}{3}\times \frac{22}{7}\times (21{)}^2\times 20[\because \pi =\frac{22}{7}]$

$=\frac{22\times 21\times 21\times 20}{21}$

$=22\times 21\times 20$

$=9240c{m}^3$

$\therefore$ Volume $=9240c{m}^3$

Now, weight of $1c{m}^3=5grams$

Hence, weight of $9240c{m}^3=9240\times 5grams$

$=46200grams$

We know that, $1000grams=1kg$

Hence, $46200grams=\frac{46200}{1000}kg$

$=46.2kg$

Hence, the weight of the given solid cone is $46.2kg$.