Question

The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 A cube of gold weighs 652 grams. Calculate the length of the edge of the cube in centimeters. Answer with two decimal places.

Answer 1

The length of the edge of the cube is 3.23 cm .

Step-by-step explanation:

We have , The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 or $y = 19.3x^3$ .  A cube of gold weighs 652 grams i.e. y = 652 . Let's calculate value of x from above data:

$y = 19.3x^3$

⇒ $y = 19.3x^3$

⇒ $652= 19.3x^3$

⇒ $19.3x^3=652$

⇒ $\frac{19.3}{19.3}x^3=\frac{652}{19.3}$

⇒ $x^3=\frac{652}{19.3}$

⇒ $\sqrt[\frac{1}{3} ]{x^3} = \sqrt[\frac{1}{3} ]{\frac{652}{19.3}}$

⇒ $({x^3})^\frac{1}{3} =({\frac{652}{19.3}})^\frac{1}{3}$

⇒ $x =(33.78)^\frac{1}{3}$

⇒ $x =3.23$

Therefore, the length of the edge of the cube  is 3.23cm.