Question

A metallic right circular cone 20 cm high and whose vertical angle is 90° is cut into two parts at the middle point of its axis by a plane parallel to the base. If the frustum so obtained be drawn into a wire of diameter (\(\frac{1}{16}\)) cm, find the length of the wire.

Answer 1

let ABC be the given cone. 

Here, 

the height of the metallic cone AO = 20 cm 

Cone is cut into two pieces at the middle point of the axis. 

hence, 

the height of the frustum cone AD = 10 cm 

Since 

∠A is right-angled, so ∠B = ∠C = 45° 

From triangle ADE,

⇒ \(\frac{DE}{AD}\) = cot 45°

⇒ \(\frac{r'}{10}\) = 1

⇒ r'=10 cm 

Similarly, 

from triangle AOB,

⇒ \(\frac{OB}{OA}\) = cot 45°

⇒ \(\frac{r"}{20}\) = 1

⇒ r'' = 20 cm 

The volume of the frustum of a cone