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

If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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If a square has a perimeter of 64 cm, what is its area?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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The probability of getting an even number when rolling a die is:

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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What is the sum of the interior angles of a hexagon?

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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