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 .

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`

⇒
`(19.3)/(19.3)x^3=(652)/(19.3)`

⇒
`x^3=(652)/(19.3)`

⇒
`\sqrt[(1)/(3) ]{x^3} = \sqrt[(1)/(3) ]{(652)/(19.3)}`

⇒
`({x^3})^(1)/(3) =({(652)/(19.3)})^(1)/(3)`

⇒
`x =(33.78)^(1)/(3)`

⇒
`x =3.23`

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