Question 1 of 13intermediate🔧 ApplyNumerical3 marks

2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.

Correct Answer

The surface area of the resulting cuboid is 160 cm².

Exercise: EXERCISE 12.1 | Q: 1 | (Page Page 6)
For More Understanding

Explanation

This question tests understanding of how surface area changes when solids are combined. When two cubes are joined end to end, the faces that are joined together are no longer part of the external surface. The resulting shape is a cuboid with dimensions derived from the original cube's side length. Students can either calculate the TSA of the cuboid directly using the formula 2(lb + bh + hl), or subtract the hidden faces from the total surface area of both cubes.

Solution Steps

  1. Step 1: Find the side of each cube. Given volume = 64 cm³. Volume of cube = (side)³. Therefore, side = ∛64 = 4 cm.

  2. Step 2: Determine dimensions of the resulting cuboid. When two cubes are joined end to end, Length = 4 + 4 = 8 cm, Breadth = 4 cm, Height = 4 cm.

  3. Step 3: Calculate total surface area of the cuboid. TSA = 2(lb + bh + hl) = 2(8×48 \times 4 + 4×44 \times 4 + 4×84 \times 8) = 2(32 + 16 + 32) = 2(80) = 160 cm².

  4. Alternative Method: Surface area of two cubes = 2×62 \times 6 × 4² = 192 cm². Area of two faces hidden during joining = 2×42 \times 4² = 32 cm². Surface area = 192 - 32 = 160 cm².

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