Answer:
353cm² of metallic sheet is used to make the bucket.
The volume of water the bucket can hold is 240cm³
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.