Q) From a solid cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is hallowed out. Find the total surface area of the remaining solid.

Ans: Let’s draw the diagram to capture the shape:

Total surface area of the cylinder:

= curved surface area of the cylinder + one side base area of the cylinder

= 2 r h + r² (one side of the base is removed in the cavity)

Given that the height of the cylinder = 20 cm and diameter of the cylinder = 12 cm, hence the radius of the cylinder = 6 cm

Hence, surface area of the cylinder = 2 (6) (20) + (6)² = 276 …. (i)

Curved surface area of the cone is given by = r l

The radius of the cone = 6 cm

The height of the cone = 8 cm

The slant height of the cone =   = 10 cm

Hence, the curved surface area of the cone = (6) (10) = 60 ………. (ii)

The surface area of the remaining solid =  Total surface area of the cylinder  + curved surface area of the cone

=  276   + 60 = 336  = (336) = 1056 m²

Therefore, the surface area of the remaining solid is 1056 m².