Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is 28 cm and height is 20 cm. Find the approximate area of the sheet required to make a lid of height 2 cm for this container.

Given:

Diameter = 28 cm

Radius height = 2 cm

As the cylindrical container is open at one side, Total area of a cylinder is given as,

Area of Cylinder = area of the base + curved surface area

Area of base = π × r²

Curved surface area = 2π × r × h

∴ Area of Cylinder = π × r² + 2π × r × h

= 3.14 × 14² + 2 × 3.14 × 14 × 20

= 615.44 + 1759.3

= 2376 cm²

Now, the area of the sheet required to make a cylindrical container is nothing but an area of the cylinder.

∴ Area of Sheet = 2376 cm²

Now, we need to make a lid for the open cylinder. Given the height of the lid is 2 cm.

As the lid is for the cylinder, it’s radius will be the radius of the cylinder.

Hence, For lid,

Radius = 14 cm

Height = 2 cm

Area of lid = area of the base of the lead + curved surface area

= π × r² + 2π × r × h

= 3.14 × 14² + 2 × 3.14 × 14 × 2

= 615.44 + 175.84

= 792 cm²

∴ Area of Sheet = 2376 cm²

∴ Area of Lid = 792 cm²