(Q9).A hemisphere is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the length of the cube. Determine the surface area of the remaining solid.

Answer:

Let the length of the edge of the cube = a units

aa

T.S.A. of the given solid = 5 × Area of each surface + Area of hemisphere

Square surface:

Side = a units

Area = a2 sq. units

5 × square surface = 5 sq. units

Hemisphere:

Diameter = a units;

Radius =
a
2

C.S.A. = 2πr2

= (
)
=
=
π
sq. units
Total surface area = 5 +
π
= (+
) sq. units.