Answer: Volume of bucket = 61544 cm³
Area of tin required = 5463.6 cm²
Step-by-step explanation:
A cone will be formed as shown in the attached photo.
The formula for determining the volume of a cone is expressed as
Volume = 1/3πr²h
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant whose value is 3.14
From the information given,
Solving the right angle triangle,
40/20 = H/(H - 21)
2 = H/(H - 21)
H = 2(H - 21)
H = 2H - 42
2H - H = 42
H = 42
For the smaller cone,
Height = 42 - 21 = 21
Volume = 1/3 × π × 20² × 21 = 2800π
For the larger cone,
Volume = 1/3 × π × 40² × 42 = 22400π
Volume of bucket = Volume of larger cone - volume of smaller cone
Volume of bucket = 22400π - 2800π = 19600π = 19600 × 3.14
Volume of bucket = 61544 cm³
Since the bucket is open, we would apply the formula for determining the curved surface area of a cone which is expressed as
Curved surface area = πrl
Where l represents the slant height
From the triangle
L² = 40² + 42² = 1600 + 1764 = 3364
L = √3364 = 58
It means that the slant height of the smaller cone is 58/2 = 29 cm
Curved surface area of larger cone is
π × 40 × 58 = 2320π cm²
Curved surface area of smaller cone is
π × 20 × 29 = 580π cm²
the area of the tin sheet required for making the bucket is
2320π - 580π = 1740π
= 1740 × 3.14 = 5463.6 cm²
