 # Question

Charlotte  has 1000 small cubes, each side measuring 1 cm.He uses these cubes to make large cubes with sides 2 cm, 3 cm,4 cm and so on.

(a)What is the length of the side of the largest cube that he can make using 729 small cubes?

(b)Find the length of the side of a cube that he made using 729 cubes.

(c) He dismantles the cube from part (b) and arranged them in the shape of a square 1 cm high with no cubes left over.What is the length of the side of the square?

a) Using 729 smaller cubes, she can make a perfect larger cube,

729 = 3 x 243
= 3 x 3 x 81
= 3 x 3 x 3 x 27
= 3 x 3 x 3 x 3 x 9
= 3 x 3 x 3 x 3 x 3 x 3
= 9 x 9 x 9
= 93

Therefore the largest cube she can form with 729 smaller cubes will have 9 cubes by 9 cubes by 9 cubes. So the length of that cube will be 9 cm.

b) Same question as a)

c) So with 729 smaller cubes, she wants to form a square.

729 = 3 x 3 x 3 x 3 x 3 x 3
= 32 x 32 x 32
= (3 x 3 x 3)2
= 272

Therefore the length of the square formed with be 27 cubes by 27 cubes. So the length of that square is 27 cm.