Answer :

after removing the conical solid the cylinder would look like this

Given: height of cylinder = height of cone = h = 15 cm

Diameter of cylinder = diameter of base cone = 16 cm

∴ radius of cylinder = radius of base of cone = 16/2 = r = 8 cm

Formula: total surface area of cylinder = 2πr^{2} + πrh

Total surface area of cone = πrl + πr^{2}

Where l is the slant height

l = √(r^{2} + h^{2})

l = √(8^{2} + 15^{2})

l = √289

l = 17 cm

In the solid as seen in figure we have the curved surface of cylinder and the base of cylinder as there is no top circular face of the cylinder we should subtract its area from total surface area of cylinder

Area of top circular surface of cylinder = πr^{2}

∴ surface area of cylinder in solid = 2πr^{2} + πrh - πr^{2}

= πr^{2} + πrh

= 3.14 × 8 × (8 + 15)

= 3.14 × 8 × 23

= 577.76 cm^{2}

Now there is a hollow conical part with no base of the cone as seen in the figure therefore we should subtract the surface area of base of cone from the total surface area of cone

Surface area of base of cone = πr^{2}

∴ Surface area of conical part in solid = πrl + πr^{2} - πr^{2}

= πrl

= 3.14 × 8 × 17

= 427.04 cm^{2}

Therefore total surface area of solid = surface area of cylinder in solid + surface area of

conical part in solid

= 577.76 + 427.04

= 1004.8 cm^{2}

Surface area of solid = 1004.8 cm^{2}

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