Given: perimeter of upper circle = 36 cm

Perimeter of lower circle = 48 cm

Height of frustum = h = 11 cm

Let r: radius of upper circle & R: radius of lower circle

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

Where l = slant height

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

∴ Perimeter of upper circle = 2πr

∴ 36 = 2 × 3.14 × r

∴ r = 36/6.28 cm

∴ r = 5.732 cm

∴ Perimeter of lower circle = 2πR

∴ 48 = 2 × 3.14 × R

∴ R = 48/6.28 cm

∴ R = 7.643 cm

∴ l = 11.164 cm

∴ Volume of frustum = (1/3) × 3.14 × 11 × (7.643² + 5.732² + 7.643 × 5.732) cm³

= (1/3) × 34.54 × (58.415 + 32.855 + 43.809) cm³

= 11.513 × 135.079 cm³

= 1555.164 cm³

∴ Volume of frustum = 1555.164 cm³

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

= 3.14 × (7.643 + 5.732) × 11.164 cm²

= 3.14 × 13.375 × 11.164 cm²

= 468.86 cm²

∴ curved surface area = 468.86 cm²