From a large cone of volume 600 cm3, a small cone is cut whose height is 70% of the height of the large cone. If the radius of the small cone is 50% of the radius of the large cone, then find the volume of the remaining part left after cutting the small cone.

From a large cone of volume 600 cm3, a small cone is cut whose height is 70% of the height of the large cone. If the radius of the small cone is 50% of the radius of the large cone, then find the volume of the remaining part left after cutting the small cone. Correct Answer 495 cm³

Let the heights of the large & small cone be ‘H’ cm & ‘h’ cm respectively

Let the radius of the large & small cone be ‘R’ cm & ‘r’ cm respectively

⇒ h = 70% of H

⇒ h/H = 7/10

Also,

⇒ r = 50% of R

⇒ r/R = 1/2

Now,

Volume of cone = Volume of cone = (1/3)π × (radius)² × Height

⇒ Volume of small cone/Volume of large cone = r²h/R²H = (1/4) × 7/10 = 7/40

⇒ Volume of small cone = 7/40 × Volume of large cone = 7/40 × 600 = 105 cm³