Vertical height of the bucket is 40 cm and that of
the cylindrical base is 6 cm. find the area of the
metallic sheet used to make the bucket, where
we do not take into account the handle of the
bucket. also, find the volume of water the
bucket can hold.

353cm² of metallic sheet is used to make the bucket.

The volume of water the bucket can hold is 240cm³

Step-by-step explanation:

SURFACE AREA

The area of the  metallic sheet used to make the bucket is the same as the surface area.

A bucket is a cylindar. The formula for surface area is SA = 2πr² + 2πrh

2πrh is the circumference of the base multiplied by the height to find the area of the middle.

πr² is the same as the area of the base. There is only one base, so we only need πr² without the 2.

πr² = 6 because it is the base.

Solve for r by isolating.

πr² = 6cm²

r² = 6cm²÷π           Divide both sides by pi

r = √(6cm² ÷ π)       Square root both sides

r ≈ 1.38cm    Rounded radius to two decimal places

Substitute the information into the formula for SA of bucket.

SA = πr² + 2πrh

SA = 6cm² + 2π(1.38cm)(40cm)

SA = 6cm² + 2π(55.2cm²)    Multiplying units make the square of the unit

SA = 352.83...cm²        Surface area of bucket, also area of metal

SA ≈ 353cm²  Round to the same nujmber of decimal places in the question

Therefore 353cm² of metallic sheet is used to make the bucket.

VOLUME

The amount of water the bucket can hold is the same as the volume.

To find the volume, use the formula for volume of a cylindar V = πr²h

πr²h is the base multiplied by the height.

Since we are given the base, we do not need to find r.

Substitute the base and the height into the formula.

V = πr²h

V = (πr²)h

V = (6cm²)40cm   Multiplying unit and unit squared makes the unit cubed

V = 240cm³    Volume of bucket

Therefore the volume of water the bucket can hold is 240cm³.

1/4 because there is 4 grades.