Given:

Radius of a cylinder(R) = 8 cm

Height of cylinder = 10 cm

Radius of cone(r) = 3 cm

Height of cone = 4 cm

Concept:

The surface area of the remaining solid will be the sum of curved surface area of the cylinder, curved surface area of the cones, and the remaining area of the two circular faces of the cylinder.

Formula used:

Curved Surface area cylinder = 2πrh

Curved Surface area Cone = πrl

Slant height of cone = √(r² + h²)

Surface area of remaining circular face of cylinder = π(R² – r²)

Where ‘R’ is outer radius

And ‘r’ is inner radius

Calculation:

Curved surface area of cylinder = 2πRh

= 2 × π × 8 × 10

= 160π cm²       ------(1)

Slant height of cone = √[(3)² + (4)²]

= √(25)

= 5cm

∴ CSA of cone on both faces = 2πrl

= 2 × 5 × 3 × π

= 30π cm²      ------(2)

Surface area of both faces of cylinder = 2π(R² – r²)

= 2π[(8)² – (3)²]

= 2π(64 – 9)

= 2π × 55

= 110π cm²       ------(3)

Adding (1), (2) and (3);

Surface area of total solid = (Curved surface area of cylinder) + (CSA of cone on both faces) + Surface area of both circular faces of cylinder)

= 160π cm² + 30π cm² + 110π cm²

= 300π cm²