Question

find the area of the aluminium sheet required to make a cyclindrical container which is open and one side and whose diameter is 42cm and height is 22cm find the approximate area of the aluminium sheet required to make a lid of height 3cm for this container​

Answer 1

Step-by-step explanation:

Diameter = 42 cm

Radius = 21 cm

Height = 22 cm

Area of Alumunium sheet required = CSA + pi r²

So,

$\sf{ \pi r ( 2h + r)}$

$\sf{ \dfrac{22}{7} \times 21 ( 2(22) + 21)}$

So, this gives out 4290 cm²

Now, approximate area of lid = CSA + pi r²

But, height is 3 cm now in this case.

$\sf{ \pi r ( 2H + r)}$

$\sf{ \dfrac{22}{7} \times 21 ( 2(3) + 21)}$

This gives out 1782 cm². Hence the answers.

Answer 2

Answer:

Given :-

◘ For cylindrical container :

• Diameter (d) = 42 cm
• Height (h₁) = 22 cm

◘ For cylindrical lid :

• Height (h₂) = 3 cm
• Diameter (d) = 42 cm

Then, the radius will be,

• Radius = Diameter/2 = 42/2 = 21 cm

Find Out :-

• Area of the cylindrical aluminium sheet required to make a cylindrical container.
• Area of the aluminium sheet required to make a lid.

Solution :-

1) Area of the cylindrical aluminium sheet required to make a cylindrical container :

⍟︎ Surface area of the cylinder with one side open = Curved surface area + Area of a base

Then,

➻ 2πrh₁ + πr²

➻ πr(2h₁ + r)

➻ 22/7 × 21(2 × 22 + 21)

➻ 22 × 3(44 + 21)

➻ 66(65)

➻ 66 × 65

➠ 4290 sq.cm

∴ The area of the cylindrical aluminium sheet required to make a cylindrical container is 4290 sq.cm.

2) Area of the aluminium sheet required to make a lid :

⍟︎ Area of sheet required to make a lid = C.S.A of lid + Area of upper surface,

Then,

➻ 2πrh + πr²

➻ πr(2h + r)

➻ 22/7 × 21(2 × 3 + 21)

➻ 22 × 3(6 + 21)

➻ 66(27)

➻ 66 × 27

➠ 1782 sq.cm

∴ The area of the aluminium sheet required to make a lid is 1782 sq.cm.