Question

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

Answer 1

Step-by-step explanation:

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:

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Edge of wooden block (a) = 21 cm

Diameter of hemisphere = edge of cube

Radius = 21/2 = 10.5 cm

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

= 6835.5 cm3

Surface area of box = 6a2 ………… (1)

Curved surface area of hemisphere = 2πr3 ……….. (2)

Area of base of hemisphere ……………….. (3)

So remaining surface area of box = (1) – (2) + (3)

= 2992.5 cm2

Remaining surface area of box=2992.5 cm2

Volume of remaining block=6835.5 cm3