An open bucket is in the form of a frustum of a cone,whose radii of bottom and top are 7 and 28cm.If the capacity of the bucket is 21560cmcube,then find the cost of metal sheet used in making the bucket at the rate of Rs. 1per10cmsq.

Answer 1

the area of metal is the area of the small circle plus the area of the sides.

The small circle has area 49π

Now for the sides. Consider the entire cone with base radius 28 and height 4h.

Chop off the top 1/4 of the height, and the missing volume is (1/3)π*7^2*h

The entire cone would have volume (1/3)π*28^2*(4h)

So, calculate the height of the bucket (3h), knowing that

π/3 (28^2*4h-7^2*h) = 21560

Now, use that height to figure the area of metal:

π*28*√(28^2+(4h)^2)-π*7√(7^2+h^2) + π*7^2