Question

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 remaining solid.​

Answer 1

SOLUTION :

Let the length of edge of cube = a

T.S.A of solid = 5×area of each surface + area of hemisphere

Square's surface :

Side = a units

Area = a² sq.units

5 × square surface = 5a² sq.units

Hemisphere :

Diameter = a units

Radius = a/2

C.S.A = 2πr²

$= 2\pi \frac{ {a}^{2} }{4}$

$\frac{\pi {a}^{2} }{2}$sq.units

Total surface area =

${5a}^{2} + \frac{\pi {a}^{2} }{2}$

${a}^{2} (5 + \frac{\pi}{2} )$sq.units

Answer 2

Let the length of cube be a

Total surface area of solid = 5 (area of each surface) + area of hemisphere

For Square -->

Surface area = side = a units

Area = a² sq.units

So,

5 × square surface = 5a² sq.units

For Hemisphere -->

Diameter = a

Radius = a/2

Curved surface area = 2πr²

= 2πa²/4

= πa²/2

Total surface area = 5 (area of each surface) + area of hemisphere

= 5a² + πa²/2 sq. units

OR

= a²(5 + π/2) sq. units