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

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

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A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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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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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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

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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 7th term of the arithmetic progression 3, 6, 9, 12,...?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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