Question 147
A 3 cm x 3 cm x 3 cm cube has three holes each of 1 cm x 1 cm cross-section running from the centre of each face to the centre of the opposite face. The total surface area (in cm$$^2$$) of the solid so obtained is
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Solution
Dimensions of cube = 3 cm x 3 cm x 3 cm and dimensions of square hole = 1 cm x 1 cm
Outer surface area of 1 face = $$(3\times3)-(1\times1)=8$$ $$cm^2$$
=> Outer surface area of the cube (6 faces) = $$6\times8=48$$ $$cm^2$$
Inner surface area of three tunnels = $$3\times2[(2\times1)+(2\times1)]=24$$ $$cm^2$$
$$\therefore$$ Total surface area of solid = $$48+24=72$$ $$cm^2$$
=> Ans - (C)
