Q. 153.7( 6 Votes )

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 = πr^{2} + πR^{2} + π(R + r)l cm^{2}

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 = πR^{2}

Surface area of bottom = πr^{2}

∴ Curved surface area = total surface area - πr^{2} - πR^{2} cm^{2}

= πr^{2} + πR^{2} + π(R + r)l - πr^{2} - πR^{2} cm^{2}

= π(R + r)l cm^{2}

= π × [(9/π) + (3/π)] × 4 cm^{2}

= (9 + 3) × 4 cm^{2}

= 48 cm^{2}

∴ curved surface area = 48 cm^{2}

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