Question

A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Determine the volume and total surface area of the remaining block.

Answer 1

Answer:

The Volume of remaining block  is 6835.5 cm³ and Total surface area of block of the remaining block is  2992.5 cm² .

Step-by-step explanation:

SOLUTION :  

Given :  

Edge of wooden block ,a = 21cm

Diameter of hemisphere = edge of cube = 21 cm

Radius = 21/2 = 10.5cm  

Volume of remaining block = volume of box – volume of hemisphere  

Volume of remaining block = a³ - ⅔ πr³

= 21³ - ⅔ × 22/7 × 10.5³

= 9261 - ⅔ × 22/7 × 10.5 × 10.5 × 10.5

= 9261 - 2 × 22 × 3.5 × 1.5 × 10.5

= 9261 - 44 × 3.5 × 1.5 × 10.5

= 9261 - 2,425.5

Volume of remaining block = 6835.5 cm³

Total surface area of box of the remaining block = Surface area of block - Area of base of hemisphere + Curved surface area of hemisphere  = 6a² -  πr² + 2πr²

Total surface area of block of the remaining block =  6a² +  πr²  

= 6 × 21² + 22/7 × 10.5 × 10.5

= 6 × 441 + 22× 1.5 × 10.5  

= 2646 + 346.5 = 2,992.5

Total surface area of block of the remaining block = 2992.5 cm²  

Hence, the Volume of remaining block  is 6835.5 cm³ and Total surface area of block of the remaining block is  2992.5 cm² .

Answer 2

$\huge\bf\pink{\mid{\overline{\underline{Your\: Answer}}}\mid}$

_______________

______

Volume of remaining block  is 6835.5 cm³

Total surface area of block of the remaining block is  2992.5 cm² .

________________

______

Step-by-step explanation:

Given,

Edge of wooden block ,a = 21cm

Diameter of hemisphere = edge of cube = 21 cm

Radius = 21/2 = 10.5cm  

now,

Volume of remaining block = volume of box – volume of hemisphere  

=> Volume of remaining block

= a³ - ⅔ πr³

putting the value of 'r',

we get,

= (21)³ - [⅔ × 22/7 × (10.5)³]

= 9261 - [⅔ × 22/7 × 10.5 × 10.5 × 10.5]

= 9261 - [2 × 22 × 3.5 × 1.5 × 10.5]

= 9261 - [44 × 3.5 × 1.5 × 10.5]

= 9261 - 2,425.5

= 6835.5

so,

Volume of remaining block = 6835.5 cm³

now,

Total surface area of box of the remaining block

= Surface area of block - Area of base of hemisphere + Curved surface area of hemisphere

= 6a² -  πr² + 2πr²

again,

Total surface area of block of the remaining block

=  6a² +  πr²  

putting the value of 'r',

we get,

= (6 × 21²) + (22/7 × 10.5 × 10.5)

= (6 × 441) + (22× 1.5 × 10.5) 

= 2646 + 346.5

= 2,992.5

therefore,

Total surface area of block of the remaining block = 2992.5 cm²  

Hence,

the Volume of remaining block  is 6835.5 cm³

and

Total surface area of block of the remaining block is  2992.5 cm² .