de cample 13 : Hanumappa and his wife Gangamma 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
22
Answers
Given :-
- Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice.
- Molass is poured into moulds in the shape of a frustum of a cone
- Frustum having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm.
- Each cm of molasses has mass about 1.2 g
To find :-
- Mass of the molasses that can be poured into each mould
Solution :-
- It is given that molass is poured into moulds in the shape of a frustum of a cone
Now, let height of frustum is h and its radii be R and r where R > r
Quantity of molasses that can be poured = volume of frustum
- Height of frustum (h) = 14cm
- Diameters of frustum = 30cm and 35cm
- Radii of frustum (r and R) = 30/2cm and 35/2cm
According to 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
Convert it by dividing 1000
- 1kg = 1000g
→ 13969.56/1000
→ 13.9kg = 14kg (approx)
Hence,
- Mass of molasses is 14kg
Answer:
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)