Topic Details (Notes format)

How to Identify and Use Perfect Cubes

Subject: Mathematics

Book: Maths Mastery

A perfect cube is an integer that is the cube of another integer, such as 27 = 3³ or 64 = 4³. Spotting these efficiently helps with factoring polynomials (like x³ – 8) or simplifying cube roots. Perfect cubes appear in 3D volume calculations, for instance, a 5×5×5 cube has a volume of 125. Understanding these patterns (1, 8, 27, 64, 125, ...) can streamline computations and deepen your exploration of algebraic identities like a³ ± b³. Whether comparing volumes or factoring expressions, perfect cubes are a potent tool in advanced math and practical tasks.

Practice Questions

A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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What is the sum of all even numbers between 1 and 50?

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What is the LCM of 15 and 20?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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What is the HCF of 48 and 180?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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The area of an equilateral triangle with side length 6 cm is:

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