Question

A bucket open at the top is in the form of a frusturn of a cone with a capacity $12308.8c{m}^3$. The radii of the top and bottom circular ends are $20cm$ and $12cm$ respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. ($Use\pi =3.14)$)

Answer 1

Given

A bucket in shape of frustum open from top having volume$=12308.8c{m}^3$

(R) radius of lower end$=12$ cm

(r) radius of upper end$=20$ cm

we know

volume$=\frac{\pi h}{3}[R^2+r^2+Rr]$

$12308.8=\frac{3.14\times h}{3}[400+144+240]$

$h=\frac{3920\times 3}{784}=15$

Hence height of frustum$=15$ cm

Now

Area of metal sheet required to make bucket

$=$CSA of frustum $+$ area of lower end circle

$A=\pi (R+r)l+\pi r^2$

where l$=$ slant height$=\sqrt{(R-r{)}^2+h^2}$

$l=\sqrt{(8{)}^2+(15{)}^2}=17$ cm

Now

area$=3.14\left[\right(20+12)17+12\times 12]$

$=3.14[544+144]=3.14\left[688\right]$

Area$=2160.32c{m}^2$

Hence $2160.32c{m}^2$ metal sheet required to make bucket.