Question

If two cubes each of volume 64 cm\(^3\) are joined end to end together, then the surface area of the resulting cuboid is:

• A. 128 cm\(^2\)
• B. 160 cm\(^2\)
• C. 192 cm\(^2\)
• D. 384 cm\(^2\)

Hint:

To find the surface area of a cuboid, use the formula \(2(lw + lh + wh)\), where \(l\), \(w\), and \(h\) are the length, width, and height, respectively.

Answer 1

The Correct Option is C

The volume of each cube is 64 cm\(^3\), so the side length of each cube is: \[ \text{Side length of cube} = \sqrt[3]{64} = 4 \, \text{cm} \] When two cubes are joined end to end, the resulting cuboid will have dimensions: \[ \text{Length} = 8 \, \text{cm}, \quad \text{Width} = 4 \, \text{cm}, \quad \text{Height} = 4 \, \text{cm} \] The surface area of a cuboid is given by the formula: \[ \text{Surface Area} = 2(lw + lh + wh) \] Substituting the values: \[ \text{Surface Area} = 2(8 \times 4 + 8 \times 4 + 4 \times 4) = 2(32 + 32 + 16) = 2 \times 80 = 160 \, \text{cm}^2 \] Thus, the correct answer is option (2).