Question

a bucket is in the form of a frustum of a cone with a capacity of 12308.8cm3.the radii of the top abottom circular ends are 20cm and 12cm respectively.find the height of the bucket and also the area of metal sheet used in making it?

Answer 1

Given that volume of the frustum(V) = 12308.8cm (cube) 

Also radii of the top (r1) = 12 cm 

Radii of the bottom (r2) = 20 cm 

We know that  

Volume of frustum 

Also we know that  

Lsquare  + h square + (r1-r2) whole square 

===> lsquare = 225 + 64 

Lsquare= 289 

L=17cm 

Now the bucket will be open at the top and so the area of the metal sheet used in making the bucket (Say A)  

A= lateral  surface of the frustum + (area of circle at the bottom with r2 = 20cm) 

A= pi(r1+r2)l +pi r square 

= 3.14x(12+20) x 17 + 3.14x (20) square 

= 3.14x32x17 + 3.14x400 

= 1708.16 + 1256 

= 2964.16 cm square