(Q4).A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. The radius of the common base is 8 cm and the heights of the cylindrical and conical portions are 10 cm and 6 cm respectively. Find the total surface area of the solid. [Use π = 3.14]

Answer:

Total surface area = C.S.A. of the cone + C.S.A. of cylinder + C.S.A of the hemisphere.

10 cm6 cmr = 8 cm

Cone:

Radius (r) = 8 cm

Height (h) = 6 cm

Slant height l = √(r2+h2)

= √(+)

= √(+)

= √()

= cm

C.S.A. = πrl

=
× ×
=
cm2

Cylinder:

Radius (r) = 8 cm;

Height (h) = 10 cm

C.S.A. = 2πrh

= ×
× ×
=
cm2

Hemisphere:

Radius (r) = 8 cm

C.S.A. = 2πr2

= ×
× ×
=
=cm2

∴ Total surface area of the given solid

=
+
+
T.S.A. =
= cm2.