Example 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 ol
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
Fig. 13
be poured into each mould.
Take T =232
Answers
The mass of the molasses that can be poured into each mould is 14 kg.
Step-by-step explanation:
It is given that,
The mould is in the shape of a frustum of a cone whose dimensions are:
The lower base diameter, d1 = 30 cm
∴ the radius, r1 = 30/2 = 15 cm
The upper base diameter, d2 = 35 cm
∴ the radius, r2 = 35/2 = 17.5 cm
The vertical height, h = 14 cm
We know that,
The quantity/volume of the molasses that can be poured into the frustum will be given by,
= The volume of the frustum
= 1/3 × π × h [r1² + r2²+ (r1×r2)]
= 1/3 × (22/7) × 14 × [(15)² + (17.5)² + (15 × 17.5)]
= (44/3) × [225 + 306.25 + 262.5]
= (44/3) × 793.75
= 11641.67 cm³
It is given that: 1 cm³ of molasses = 1.2 g
Thus,
The mass of the molasses that can be poured into each mould is,
= 11641.67 × 1 2
= 13970.004 g
[∵ 1g = 1/1000 kg]
= 13970.004/1000
= 13.97 kg
≈ 14 kg (approx)
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Ram and mehmood are two neighbours ram wears a cap which is in the shape of a hemisphere of radius 7 cm and mehmood wears a turkish cap which is in the shape of a frustum of a cone if the radius of its open side is 10 cm and the radius of the upper base is 4 cm and its slant height is 15 cm find the curved surface area of the both cape?
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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)