Question

The diameter of lower and upper of hands of bucket of a farm of frustom of a cone are 10cm and 30 cm .If itsheight is 24cm .Find (i) the area of metal sheets used to make bucket (ii) Why are should award bucket made by ordinary plastic? (π = 3.14)

Answer 1

Diameter of upper end of bucket ,d₁ = 30cm
so, radius of upper end of bucket , r₁ = 15cm
Diameter of lower end of bucket , d₂ = 10cm
so, radius of lower end of bucket , r₂ = 5cm
height of bucket , h = 24cm
lateral length of bucket , L = √(h² + (r₁-r₂)²}
=√{24² + (15-5)²}=√(576+100)=26cm

So, the area of metal sheet require to make it = π(r₁ + r₂)L + πr₁²
= π(15 + 5) × 26 + π(5)²
= π × 20 × 26 + 25π
= 520π + 25π
= 545π
= 545 × 3.14
= 1711.3 cm²

Answer 2

Solution :-

Diameter of the upper end = 30 cm

Radius, r1 = 30/2 = 15 cm

Diameter of the lower end = 10 cm

Radius, r2 = 10/5 = 5 cm

Height = 24 cm

Slant height of the bucket l = √h² + (r1 - (r2)²

⇒ √24² + (15 - 5)²

⇒ √576 + 10²

⇒ √576 + 100

⇒ √676

l = 26 cm

Slant height is 26 cm

Total surface area of the metal sheet = π(r1 + r2)l + πr2²

⇒ 22/7*26*(15 + 5) + 22/7*5*5

⇒ 22*520/7 + 550/7

⇒ 11440/7 + 550/7

⇒ 1634.28 cm² + 78.57

= 1712.85 cm²

So, area of the metal sheet used to make the bucket is 1712.85 cm²

Answer.