Question

THE diameter of the lower and upper end of a bucket in a form of a frustum of a cone are 10cm and 30 cm . if its height is 24 cm.find the area of metal sheet required to make it

Plz tell me fast kl exam h mera

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 =$\sqrt{h^2+(r_1-r_2)^2}$
=$\sqrt{24^2+(15-5)^2}=\sqrt{576+100}=26cm$

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 × 22/7
= 11990/7
= 1712.85 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 cm²

= 1712.85 cm²

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

Answer.