Question:
Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm, supposing the material of which it is made weighs 10 grams per cubic cm.
Solution:
It is given that:
Diameter (d) = 14 cm
Height of the cone (h) = 51cm
Radius of the cone(r) = d/2
= 14/2 = 7cm
Therefore, Volume of cone $(v)=1 / 3 \pi r^{2} h$
$=1 / 3 * 3.14 * 7 * 5 * 51=2618 \mathrm{~cm}^{3}$
Now it is given that $1 \mathrm{~cm}^{3}$ material weighs $10 \mathrm{gm}$.
Therefore, $2618 \mathrm{~cm}^{3}$ weighs $=2618$ * $10=26180$ grams.