Question

A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, then find the height of the bucket.

Answer 1

We have,

Radius of upper end, R=28 cm and

Radius of lower end, r = 21 cm

Let the height of the bucket be h.

Now,

Volume of water the bucket can hold = 28.49 L

⇒ Volume of bucket = 28490 cm³    (As, 1L = 1000 cm³)

`rArr 1/3pi"h"("R"^2+"r"^2+"Rr") = 28490`    

`rArr 1/3xx22/7xx"h"(28^2+21^2+28xx21) = 28490`

`rArr (22"h")/21xx49xx(16+9+12)=28490`

`rArr (22"h")/3 xx7xx37 = 28490`

`rArr "h" = (28490xx3)/(22xx7xx37)`

∴ h = 15 cm

So, the height of the bucket is 15 cm.