Question

The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88m². Find the dimensions?

• A. 2m, 4m, 6m
• B. 1m, 2m, 3m
• C. 5m, 10m, 15m
• D. 3m, 2m, 1m

Answer 1

Answer:

A. 2m, 4m, 6m

Total Surface Area (TSA) of a Cuboid

• The Total Surface Area (TSA) of a cuboid is the sum of the areas of all its six rectangular faces.

• The formula for the Total Surface Area of a cuboid is given by: TSA = 2(lb + bh + hl), where 'l' is length, 'b' is breadth, and 'h' is height.

• Substituting the ratio-based dimensions (x, 2x, 3x) into the formula:

  • TSA = 2[(x)(2x) + (2x)(3x) + (3x)(x)]

  • TSA = 2[2x² + 6x² + 3x²]

  • TSA = 2[11x²]

  • TSA = 22x²

Solving for the Unknown and Dimensions

• Given that the Total Surface Area is 88 m², we can set up the equation: 22x² = 88.

• To find 'x', divide both sides by 22: x² = 88 / 22, which simplifies to x² = 4.

• Taking the square root of both sides, x = √4. Since dimensions must be positive, x = 2.

• Now, substitute the value of 'x' back into the ratio-based dimensions:

  • Length (l) = x = 2 m

  • Breadth (b) = 2x = 2(2) = 4 m

  • Height (h) = 3x = 3(2) = 6 m