Answer :

Given: perimeter of upper circle = 18 cm


Perimeter of lower circle = 6 cm


Slant height of frustum = l = 4 cm


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


Let r be the radius of lower circle and R be the radius of upper circle


Now perimeter of circle = circumference of circle = 2π × radius


Perimeter of upper circle = 2πR


18 = 2 × π × R


R = 9/π cm


Perimeter of lower circle = 2πr


6 = 2 × π × r


r = 3/π cm


Now we have asked curved surface area, so we should subtract the top and bottom surface areas which are flat circles.


Surface area of top = πR2


Surface area of bottom = πr2


Curved surface area = total surface area - πr2 - πR2 cm2


= πr2 + πR2 + π(R + r)l - πr2 - πR2 cm2


= π(R + r)l cm2


= π × [(9/π) + (3/π)] × 4 cm2


= (9 + 3) × 4 cm2


= 48 cm2


curved surface area = 48 cm2


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