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 (i) The area of the metal sheet used to make the bucket?

Given: Height of the frustrum(h)=24cm
radius of lower end of bucket(r1)=10/2=5cm
Radius of upper end of bucket(r2)=30/2=15cm
∴Slant height(l)=√h²+(r2−r1)²=√(24)²+(15−5)²=√(24)²+(10)²=√576+100=√676=26cm
Now, Area of the metal sheet used to make the bucket = T.S.A of the bucket (excluding the upper end)
Total Surface Area(TSA)=π(r1+r2)l+πr1²=(3.14)(15+5)(26)+3.14(5)²=1632.8+78.5=1711.3cm²(b) We should avoid the bucket made by ordinary plastic as plastic is non biodegradable and hazardous to environment.