Q. 284.0( 16 Votes )

Answer :

Length of cubical piece of wood = a = 21 cm

Volume of cubical piece of wood = a^{3}

= 21 × 21 × 21 cm^{3}

= 9261 cm^{3}

Surface area of cubical piece of wood = 6a^{2}

= 6 × 21 × 21 cm^{2}

= 2646 cm^{2}

Since, a hemisphere is carved out in such a way that the diameter of the hemisphere is equal to the side of the cubical piece.

So, diameter of hemisphere = length of side of the cubical piece

Diameter of hemisphere = 21 cm

Radius of hemisphere = r = Diameter ÷ 2 = 21/2 cm = 10.5 cm

Volume of hemisphere = 2/3 πr^{3}

= 2/3 × 22/7 × 10.5 × 10.5 × 10.5 cm^{3}

= 2425.5 cm^{3}

Surface area of hemisphere = 2πr^{2}

= 2 × 22/7 × 10.5 × 10.5 cm^{2}

= 693 cm^{2}

A hemisphere is carved out from cubical piece of wood

Volume of remaining solid = Volume of cubical piece of wood – Volume of hemisphere

Volume of remaining solid = 9261cm^{3} – 2425.5 cm^{3} = 6835.5 cm^{3}

Surface area remaining piece of solid = surface area of cubical piece of wood – Area of circular base of hemisphere + Curved Surface area of hemisphere

Surface area remaining piece of solid = 6a^{2} – πr^{2} + 2πr^{2}

= (2646 – 22/7 × 10.5^{2} + 693) cm^{2}

= 2992.5 cm^{2}

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