**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 + r^{2 }(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 m^{2}

**Therefore, the surface area of the remaining solid is 1056 m ^{2}.**