Question

Dome of the enemy's fort is in the shape of a right cone which has slant height 13 m and height of 12 m as observed by the hero through the telescope.Hero comes to know that the dome is filled with gold. If the cost of gold is$\frac{30}{\pi }$lakhs per cubic meter, then find the total value of gold in the dome of the enemy's fort.(Take $\pi$= $\frac{22}{7}$)

Answer 1

From the relation $l^2$ =$h^2$ +$r^2$

$\Rightarrow$ r = $\sqrt{l^2-h^2}$

$\Rightarrow$ r = $\sqrt{169-144}$

$\Rightarrow$ r = 5m

Volume of the dome of the fort=$\frac{1}{3}\pi r^{2}h=100\pi$

Total cost of the gold in the enemy’s fort =$100\pi \times \frac{30}{\pi }$ lakhs per cubic meter = $30$ crores units