Question

from a cubical piece of wood of side 21cm , a hemisphere is curved out in such a way that the diameter of the hemisphere is equal to the side of cubical piece find the surface area and volume of the remaining piece

Answer 1

Cubical volume =21*21*21=9261cm3
cubical surface area =6*21*21=2646cm2
diameter = side of cubical piece
radius =diameter/2
r=21/2=10.5cm
volume of new side =10.5*10.5*10.5=1157.625cm3
surface area of new side =6*10.5*10.5=661.5cm2
volume of remaining piece =9261-1157.625=8103.375cm2
surface area remaining piece 2646-661.5=1984.5cm2

Answer 2

Answer:

Surface area of remaining piece = 1953 cm²

Volume of the remaining piece = 6835.50 cm³

Step-by-step explanation:

Side of cubical piece = 21 cm

Surface area of the piece = 6·side²

⇒ Surface area = 6 × 21²

⇒ Surface Area = 2646 cm²

Volume of the piece = side³

⇒ Volume = 21³

⇒ Volume = 9261 cm³

Diameter of curved out hemisphere = 21 cm

⇒ Radius = 10.5 cm

Surface area of curved out hemisphere = 2π × radius²

⇒ Surface Area = 693 cm²

$\text{Volume of curved out hemisphere = }\frac{2}{3}\pi\times radius^3\\\\\implies Volume = 2425.5\text{ cm}^3$

Surface area of remaining piece = 2646 - 693

                                                      = 1953 cm²

Volume of the remaining piece = 9261 - 2425.50

                                                    = 6835.50 cm³