The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone
The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:
- The area of the metal sheet used to make the bucket.
- Why we should avoid the bucket made by ordinary plastic? [Use π = 3.14]
Answer
Given:
Diameter of upper end of bucket = 30 cm
Radius of the upper end of the frustum of cone, r1 = 15 cm
Diameter of lower end of bucket = 10 cm
Radius of the lower end of the frustum of cone, r2 = 5 cm
Height of the frustum of Cone, h = 24 cm
Slant height of bucket, L = √[(h² + (r1 - r2)²]
L = √[24² + (15 - 5)²]
L = √(576 + 10²)
L = 26 cm
Area of metal sheet = Curved Surface Area of bucket + area of lower end
= π(r1 + r2)L + πr2²
= 3.14(15 + 5) × 26 + π(5)²
= 3.14 × 20 × 26 + 25 × 3.14
= 1711.3 cm²
Hence, the Area of metal sheet used to make the bucket is 1711.3 cm².
ii. We should avoid bucket made by ordinary plastic because it is non-biodegradable. It makes soil less fertile and also pollute the environment.