A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height and the base radius of the cone are also the same. Find the whole surface and volume of the remaining cylinder.
Radius of cylinder(r) = 5 cm
Height of cylinder, (h) = 12 cm
Let, l be slant height of cone
Slant height of the cone = =13 cm
Volume of cylinder = π × × 12 = 300 cm3
Volume of the conical hole = × π × 5 × 12 = 100 cm3
Therefore, Volume of the remaining solid
= Volume of the cylinder – Volume of the removed conical part
= 300 π -100 π = 200 π cm3
Curved surface of the cylinder
= 2 × π r h = 2 × π × 5 × 12 = 120π cm
Curved surface of cone = π r l = π × 5 × 13 = 65π cm
Base area of cylinder = π × 52 = 25cm2
The whole surface area of the remaining solid includes the curved surface of the cylinder and cylinder and the cone and area of the base
Therefore, Whole surface area = 120 π + 65π + 25π =210π cm2