Question

a hemispherical depression is cut out from one face to cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. determine the surface area of the remaining solid​

Answer 1

Answer:

Consider the diagram shown below.

It is given that a hemisphere of radius

2

l

is cut out from the top face of the cuboidal wooden block.

Therefore, surface area of the remaining solid

= surface area of the cuboidal box whose each edge is of length l − Area of the top of the hemispherical part + curved surface area of the hemispherical part

=6l

2

−πr

2

+2πr

2

=6l

2

−π(

2

l

)

2

+2π(

2

l

)

2

=6l

2

−

4

πl

2

+

2

πl

2

=

4

l

2

(24+π) sq.units

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Consider the diagram shown below.

It is given that a hemisphere of radius

2

l

is cut out from the top face of the cuboidal wooden block.

Therefore, surface area of the remaining solid

= surface area of the cuboidal box whose each edge is of length l − Area of the top of the hemispherical part + curved surface area of the hemispherical part

$= 6l ^{2} - \pi \: r^{2} - + 2\pi \: r^{2}$

$= 6l^{2} - \pi(1 \div 2){1 \div 2} + 2\pi(1 \div 2){1 \div 2}$

$= 6l^{2} - (\pi \: l^{2} ) \div 4 + (\pi \: l^{2} ) \div 2$

$= (l^{2} \div 4) (24 + \pi) \: sq.unit$

ᕼOᑭᗴ IT ᕼᗴᒪᑭՏ YOᑌ

(24+π) sq.units