Properties of Cubes Quiz - CBSE Class 8 Mathematics

Free practice quiz: Properties of Cubes (CBSE Class 8 Mathematics). 13 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

Sample questions

1. Which of the following numbers is a perfect cube?

   1. 8
   2. 12
   3. 15
   4. 20
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   Answer: A. 8

   8 is a perfect cube because 2 x 2 x 2 = 8.

2. What is the smallest perfect cube that is divisible by 9?

   1. 27
   2. 81
   3. 64
   4. 125
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   Answer: A. 27

   27 is a perfect cube (3³) and is divisible by 9 (27/9 = 3).

3. What is the sum of the cubes of the first three natural numbers?

   1. 9
   2. 18
   3. 27
   4. 36
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   Answer: D. 36

   1³ + 2³ + 3³ = 1 + 8 + 27 = 36

4. If n is a natural number, then n³ + 1 is divisible by which of the following?

   1. n+1
   2. n-1
   3. n+2
   4. n-2
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   Answer: A. n+1

   Use the identity a³ + b³ = (a+b)(a²-ab+b²). Here, a=n and b=1. Thus, n³+1 = (n+1)(n²-n+1)

5. Find the smallest number by which 1728 must be multiplied to make it a perfect cube.

   1. 1
   2. 2
   3. 3
   4. 4
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   Answer: A. 1

   1728 = 12³ Therefore, it is already a perfect cube.

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