Question
Download Solution PDFA cube of side 5 cm, has been assembled using 125 cubes each of 1 cm edge. One cube is removed from the middle of each of the faces of the cube. What is the surface area (in cm2) of the remaining solid?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Side of a larger cube (a) = 5 cm
Side of each smaller cube (b) = 1 cm
Formulae used:
Surface area of a cube = 6(side)2
Change in surface area when one cube is removed = 5(side length of the smaller cube)2 - 1 × (side length of the smaller cube)2
Solution:
The surface area of the larger cube = 6a2
⇒ 6 × 52 = 6 × 25 = 150 cm2
Increase in surface area when one cube is removed = 5 × b2 - 1 × b2
⇒ 4 × (1 cm)2 = 4 cm2
Total increase in surface area after removing one cube from each face of the larger cube = 6 × (increase in area)
⇒ 6 × 4 cm2 = 24 cm2
The overall surface area of the remaining shape is = original surface area + Total increase in surface area
150 cm2 + 24 cm2 = 174 cm2.
∴ Option 4 is the correct answer.
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