The 3D solid given below has edges of equal length of 16 cm. A rectangular hole of dimensions 4x3 cm and depth 2 cm is made in the centre of each face. Calculate the total surface are of the resulting solid in square cm.
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Given : A solid cube with edges of equal length of 16 cm. A rectangular hole of dimensions 4x3 cm and depth 2 cm is made in the centre of each face.
To Find : total surface are of the resulting solid in square cm
Solution:
Surface area of cube =6 x 16² = 1536 cm²
4x3 cm holes on each Face reduced = 12 * 6 = 72 cm²
Hence Area = 1536 - 72 = 1464 cm²
Now surface area created because of depth of 2 cm
= 6 * ( 4 * 3 + ( 4*2 + 3*2) * 2 )
= 6 ( 12 + 28)
= 240 cm²
Total Surface Area = 1464 + 240 = 1704 cm²
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