Given: Radius of the hemisphere = 6 cm Diameter of base of hemisphere = Diameter of base of cone Formula used: Volume of hemisphere = 2πr3/3 Volume of cone = πr2h/3 As cone is inscribed in the hemisphere so, the height of the cone will be equal to the radius of the hemisphere Calculation: Radius of the base of hemisphere = 6 cm ⇒ Volume of hemisphere = 2π × 6 × 6 × 6/3 cm3 = 144π cm3 Now, Radius of cone = radius of hemisphere = 6 cm Height of cone = 6 cm ⇒ Volume of cone = π × 6 × 6 × 6/3 cm3 = 72π cm3 Now, Volume of the remaining part = Volume of hemisphere – volume of cone ⇒ Volume of the remaining part = 144π cm3 – 72π cm3 = 72π cm3 ∴ Ratio of Volume of hemisphere and Volume of remaining part = 144π : 72π ⇒ 2 : 1 Short Trick: Radius of both hemisphere and cone is equal and the height of the cone will also be equal to the radius of the hemisphere So, h = r = 6 cm Volume of the remaining part = 2πr3/3 – πr3/3 (as r = h) ⇒ Volume of the remaining part = πr3/3 ⇒ π6 × 6 × 6/3 = 72π cm3 ∴ Ratio of Volume of hemisphere and Volume of remaining part = 144π : 72π ⇒ 2 : 1