A bucket open at the top and bottom radii of circular ends as 40 cm and 20 cm respectively. Find the volume of the bucket if its
depth is 21 cm.Also find the area of the tin sheet required for making the bucket.
1 answer:
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
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