Question

Three cubes with volumes 8 cm3, 27 cm3 and 64 cm3 are glued together to form a solid figure. What the least possible surface area (cm2) of the solid figure?

Answer 1

☆Answer :

3Cubes :

1. Volume = 8cm³ ==> r = 2cm
2. Volume = 27cm³ => r = 3cm
3. Volume = 64cm³ => r = 4cm

Soo :

Volume - 1 = 6 × 2² = 6 × 4 = 24cm²

Volume - 2 = 6 × 3² = 6 × 9 = 54cm²

Volume - 3 = 6 × 4² = 6 × 16 = 96cm²

• Totals = 24 + 54 + 96 = 174cm²

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surface area = 174 - 2(3² + 2²)

surface area = 174 - 2(9 + 4)

surface area = 174 - 2(13)

surface area = 174 - 26

serface area = 148cm²

`\:`

-HayabusaBrainly

Answer 2

• 148 cm²

Explanation:

The cubes have sides of 2 cm, 3 cm and 4 cm respectively.

Their face area of the cubes is 4 cm², 9 cm² and 16 cm² respectively.

Total surface area of each cube is:

• Side 2 cm - 6*(2*2) = 24 cm²,
• Side 3 cm - 6*(3*3) = 54 cm²,
• Side 4 cm - 6*(4*4) = 96 cm².

Total of three cubes:

• 24 + 54 + 96 = 174 cm²

When you glue the cubes together you lose an area equal to double face area of the smaller cube from the total surface area.

Possible decrease, provided full faces area covered:

• 2 cm cube with the other two ⇒ loss of four 2x2 faces 4*4 = 16 cm²
• 3 cm or 4 cm cube with the other two ⇒ loss of two 3x3 and two 2x2 faces 2(9+4) = 26 cm²

The least possible surface area is:

• 174 - 26 = 148 cm²