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When the length of each edge of a cube is increased by 1 cm, the volume is increased by 37 cm3.
What is the length (in centimeters) of each edge of the original cube?

When the length of each edge of a cube is increased by 1 cm the volume is increased by 37 cm3 What is the length in centimeters of each edge of the original cub class=

Respuesta :

original length =3cm

Answer:

solution given;

let length be x

its

volume be x ³

we have when length is increased by 1cm volume increased by 37cm³ so

(x+1)³=x³+37cm³

x³+1³+3x²+3x=x³+37

3x²+3x-36=0

3(x²+x-12)=0

x²+4x-3x-12=0

x(x+4)-3(x+4)=0

(x+4)(x-3)=0

either

x=-4 rejected

or

x=3cm

The length (in centimeters) of each edge of the original cube will be 3.

How do you calculate the volume of a cube?

Assume the side length of the cube under consideration is L units. The volume of the cube is then equal to L³ cubic units.

We have when length is increased by 1 cm volume increased by 37 cm³, so from the given condition the equation formed as;

(L+1)³=L³+37 cm³

Open the bracket and apply the necessary identities;

L³+1³+3L²+3L=L³+37

3L²+3L-36=0

3(x²+x-12)=0

Applying the factorization method;

L²+4L-3L-12=0

L(L+4)-3(L+4)=0

(L+4)(L-3)=0

L=-4 cm (Negative length is not possible.)

L=3cm

Hence,the length (in centimeters) of each edge of the original cube will be 3.

Learn more about volume of cube refer:

https://brainly.com/question/26136041

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