Topic Details (Notes format)

How to Calculate the Diagonal of a Cuboid

Subject: Mathematics

Book: Maths Mastery

For a cuboid (rectangular prism), the space diagonal that stretches from one vertex to the opposite vertex is given by d = √(L² + W² + H²), where L, W, and H are length, width, and height. For instance, if a box is 3 m × 4 m × 12 m, the diagonal is √(3² + 4² + 12²) = √(9 + 16 + 144) = √169 = 13 m. This formula is used in warehouse logistics (checking if a box can fit diagonally), 3D geometry tasks, and advanced engineering designs requiring precise spatial measurements.

Practice Questions

If x = 3 and y = 4, what is the value of x^2 + y^2?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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If sin(A) = 1/2 and A is acute, what is the value of A?

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If the probability of an event is 1/4, what is the probability of its complement?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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What is the HCF of 72 and 120?

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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