Can you please find the answer to the question If both base radius and height of a cone are equal to the radius of the hemispherical bowl, then ______ coneful of water is required to fill up the vessel. Options: A) 2 , B) 4 , C) 3 ,D) 6 (My maths teacher has asked this)
Solution Let 'r' be the radius of the hemispherical bowl (which is also the base radius and height of the cone). Volume of hemisphere = (2/3)πr³ Volume of cone = (1/3)πr²h since, h=r. Then, the volume of cone becomes (1/3)πr³. To obtain the number of cones to fill the hemispherical bowl: Dividing the volume of the hemisphere by volume of cone, we have (volume of hemisphere)/(volume of cone) = (2/3)πr³ / (1/3)πr³ = 2/3 ÷ 1/3 = 2/3 × 3/1 = 2 Option (A) 2
