Question

The surface area of a cuboid is 632 m² and the three sides are in the ratio 3:5:8. Find the dimensions.​

Answer 1

Answer :

• Dimensions are 6m , 10m and 16m

Given :

• Surface area of a cuboid is 632 m²
• Three sides are in the ratio 3:5:8

To find :

• Dimensions

Solution :

• Let the length be 3x
• Breadth = 5x
• Height = 8x

Given , surface area of a cuboid is 632

As we know that,

• Total surface area of cuboid = 2(lb + bh + lh)

where, l is length 3x , b is breadth 5x and h is height 8x

》Total surface area of cuboid = 2(lb + bh + lh)

》632 = 2((3x)(5x) + (5x)(8x) + (3x)(8x))

》632 = 2(15x² + 40x² + 24x²)

》 632 = 2(79x²)

》632 = 158x²

》x² = 632/158

》x² = 4

》x = 2

• Length = 3x = 3(2) = 6m
• Breadth = 5x = 5(2) = 10m
• Height = 8x = 8(2) = 16m

Hence , Dimensions are 6m , 10m and 16m

Answer 2

Given :

• Ratio of the sides of the cuboid = 3:5:8
• Total Surface Area of Cuboid = 632m²

To Find :

• Dimensions of the Cuboid.

Solution :

✰ As we know that, Total Surface Area of Cuboid is given by 2 (lb + bh + hl) . Now in this question Total Surface Area of Cuboid and the ratio of length, breadth and height are given so we will assume the length, breadth and height as 3p , 5p , 8p respectively. Now simply we will put the given values in the formula to find the dimensions.

⠀⠀⠀

⟼ TSA = 2(lb + bh + hl)

⟼ 632 = 2(3p × 5p + 5p × 8p + 8p × 3p)

⟼ 632 = 2(15p² + 40p² + 24p²)

⟼ 632/2 = 15p² + 40p² + 24p²

⟼ 316 = 15p² + 40p² + 24p²

⟼ 316 = 15p² + 64p²

⟼ 316 = 79p²

⟼ 316/79 = p²

⟼ 4 = p²

⟼ √4 = p

⟼ 2 = p

⠀

Therefore :

⟿ Length of Cuboid = 3p

⟿ Length of Cuboid = 3 × 2

⟿ Length of Cuboid = 6m

⠀

⟿ Breadth of Cuboid = 5p

⟿ Breadth of Cuboid = 5 × 2

⟿ Breadth of Cuboid = 10m

⠀

⟿ Height of Cuboid = 8p

⟿ Height of Cuboid = 8 × 2

⟿ Height of Cuboid = 16m

⠀

Thus Length, Breadth and Height of the Cuboid are 6m , 10m and 16m respectively.

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