31.

Identify the open-ended problem.

(1) Parikshit makes a cuboid of dimensions 5 cm, 2 cm and 5 cm. How many such minimum cuboids are required to form a cube?

(2) Find the cube-root of 512 using prime factorization method

(3) Find the cube of 10

(4) Write any 5 numbers whose cube is more than 64

Given dimensions of cuboid are 5 cm, 2 cm and 5 cm.

Here LCM of 5, 2 and 5 is 10

5 x 2 = 10

2 x 5 = 10

5 x 2 = 10

Hence, the minimum number of cuboid require to form a cube = 2 x 5 x 2 = 20

Since it has more than one correct answers of it is open-ended problem

2.

512 = 8 x 8 x 8 = (4 x 2) x (4 x 2) x (4 x 2) =(2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2)

:.Cube root of 512 = 8

Since it has more than one ways for pairing so it is open ended problem.

3. 10 = 2 x 5 Cube of 10 = (10)³ or (2 x 5)³

Since it has more than one ways for finding cube so it is open-ended problem

4. Numbers whose cube is more than 64 are 5, 6, 7, 8, 9 Since it has more than one correct answers so it is open-ended problem.