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 cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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What is the cube of 4?

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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If the sum of three consecutive integers is 72, what are the integers?

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If the sum of three consecutive integers is 96, what are the integers?

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

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The LCM of 12 and 15 is:

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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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 the radius of a circle is doubled, what happens to its area?

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