Question

answers in detail plz

Answer 1

Answer:

7.8 cm

Step-by-step explanation:

Let the side of the cube be S.

Volume of a cube = (Side) ^3

As given,

S^3 = 474.552

S = (474.552) ^ (1/3)

(A power of 1/x means the root of x. Hence, a power of 1/3 means a root of 3 i.e. a cube root).

S = 7.8 cm

Following is the prime factorisation of 474.552 :

(474552) / ( 1000)

= ( 2 × 2 × 2 × 3 × 3 × 13 × 13 × 13 ) / ( 10 × 10 × 10)

= ( 2^3 × 3^3 × 13^3 ) / ( 10^3 )

Thus, 474.552 ^ (1/3) =

{( 2^3 × 3^3 × 13^3 ) ^ 1/3} / {( 10^3) ^

1/3}

= ( 2 × 3 × 13 ) / ( 10 )

= ( 78 ) / ( 10 )

= 7.8