Sivnath and his wife Ganga are busy
making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which
is poured into moulds in the shape of a frustum of a cone
having the diameters of its two circular faces as 30 cm
and 35 cm and the vertical height of the mould is 14 cm
(see Fig. 13.22). If each cm of molasses has mass
about 1.2 g, find the mass of the molasses that can be
poured into each mould.
(answers in pls)
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Height of frustum (h) = 14cm
Diameters of frustum = 30cm and 35cm
Radii of frustum (r and R) = 30/2cm and 35/2cm
volume of frustum = ⅓ πh(R² + r² + Rr)
→ ⅓ × 22/7 × 14[(35/2)² + (30/2)² + 35/2 × 30/2]
→ ⅓ × 22 × 2[1225/4 + 900/4 + 17.5 × 15]
→ ⅓ × 22 × 2[1225/4 + 900/4 + 17.5 × 15]
→ ⅓ × 22 × 2[1225/4 + 900/4 + 262.5]
→ 44/3[1225 + 900 + 1050/4]
→ 44/3 × 3175/4
→ 11 × 1058.3
→ 11641.3 cm³
Each cm³ of molasses has mass about 1.2 g
→ Mass of 11641.3cm³
→ 11641.3 × 1.2
→ 13969.56 g
→ 13969.56/1000 (1kg = 1000g )
→ 13.9kg = 14kg (approx)
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