Sample 13: Hanumappa and his wife Gangamma aremaking jaggery out of su

1.	Sample 13: Hanumappa and his wife Gangamma aremaking jaggery out of sugarcane juice. They haverocessed the sugarcane juice to make the molasses,hich is poured into moulds in the shape of a frustum ofacone having the diameters of its two circular faces as30 cm and 35 cm and the vertical height of the mould is14 cm (see Fig. 13.22). If each cm of molasses hasmass about 1.2 g, find the mass of the molasses that canFig. 13.22
Answer» Please like the solution 👍 ✔️ Given, mould is in the shape of a frustum of a cone in which r2= 30/2, r1=35/2 cm, h= 14 cm. Quantity (volume) molasses that can be poured into it= volume of the frustum = π/3 × h (r1² + r2²+r1r2)= 1/3×(22/7) × 14 [(35/2)²+(30/2)²+(35/2 × 30/2]= 44/3[ 306.25 + 225 +262.5]= 44/3 × 793.75= 11641.7 cm³ Given : 1 cm³ of molasses = 1.2 g Mass of the molasses that can be poured into each mould= 11641.7 × 1 2 = 13970.04 g= 13970.04/1000= 13.97 kg [ 1g = 1/1000 kg] Hence, Mass of the molasses that can be poured into each mould= 13.97 kg= 14 kg (approx)

Sample 13: Hanumappa and his wife Gangamma aremaking jaggery out of sugarcane juice. They haverocessed the sugarcane juice to make the molasses,hich is poured into moulds in the shape of a frustum ofacone having the diameters of its two circular faces as30 cm and 35 cm and the vertical height of the mould is14 cm (see Fig. 13.22). If each cm of molasses hasmass about 1.2 g, find the mass of the molasses that canFig. 13.22

Answer»

Please like the solution 👍 ✔️

Given, mould is in the shape of a frustum of a cone in which r2= 30/2, r1=35/2 cm, h= 14 cm.

Quantity (volume) molasses that can be poured into it= volume of the frustum

= π/3 × h (r1² + r2²+r1r2)= 1/3×(22/7) × 14 [(35/2)²+(30/2)²+(35/2 × 30/2]= 44/3[ 306.25 + 225 +262.5]= 44/3 × 793.75= 11641.7 cm³

Given : 1 cm³ of molasses = 1.2 g

Mass of the molasses that can be poured into each mould= 11641.7 × 1 2 = 13970.04 g= 13970.04/1000= 13.97 kg

[ 1g = 1/1000 kg]

Hence, Mass of the molasses that can be poured into each mould= 13.97 kg= 14 kg (approx)