Given: height of container frustum = h = 16 cm

Radius of lower circular end = r = 8 cm

Radius of upper circular end = R = 20 cm

Cost of 100 cm2 metal sheet = 15 Rs

Cost of 1 cm2 metal sheet = 15/100 = 0.15 Rs

Formula: Total surface area of frustum = πr2 + πR2 + π(R + r)l cm2

Where l = slant height

l = 20 cm

Since it is given that a bucket is to be made hence the top is open we need to subtract the area of top/upper circle from total surface area of frustum because we don’t require a metal plate for top.

Radius of top/upper circle = R

Area of upper circle = πR2

area of metal sheet used = (total surface area of frustum)-πR2

= πr2 + πR2 + π(R + r)l- πR2 cm2

= πr2 + π(R + r)l cm2

= π × (82 + (20 + 8)20) cm2

= 3.14 × 624 cm2

= 1959.36 cm2

1959.36 cm2 metal sheet is required to make the container.

Cost of 1959.36 cm2 metal sheet = 1959.36 × cost of 1 cm2 metal sheet

= 1959.36 × 0.15 Rs

= 293.904 Rs

Cost of metal sheet required to make container = 293.904 Rs

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