A bucket open at the top is in the form of a frusturn of a cone with a capacity 12308.8 cm3. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (Use π=3.14))
Given
A bucket in shape of frustum open from top having volume=12308.8cm3
(R) radius of lower end=12 cm
(r) radius of upper end=20 cm
we know
volume=πh3[R2+r2+Rr]
12308.8=3.14×h3[400+144+240]
h=3920×3784=15
Hence height of frustum=15 cm
Now
Area of metal sheet required to make bucket
=CSA of frustum + area of lower end circle
A=π(R+r)l+πr2
where l= slant height=√(R−r)2+h2
l=√(8)2+(15)2=17 cm
Now
area=3.14[(20+12)17+12×12]
=3.14[544+144]=3.14[688]
Area=2160.32cm2
Hence 2160.32cm2 metal sheet required to make bucket.