It takes one kilogram of metal to make a certain solid cube. What mass of metal is needed to make a cube of the same metal whose edge is twice as long as the first? Explain your answer.

4 Answers | Add Yours

lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

To solve this, apply the formula of density.

`rho=m/V`

where `rho` is the density, m is the mass and V is the volume.

Then, consider the first cube.

Let the edge of the first cube be x. So the volume of the first cube is:

`V_1=x^3`

Since the mass of the first cube is 1kg, its density is:

`rho_1=1/x^3`

Then, consider the second cube. Since its edge is twice as long as the first cube, then the length of the sides of the second cube is 2x. So, its volume will be:

`V_2=(2x)^3 = 8x^3`

Also, since its mass is unknown, let it be m2. Hence, the density of the second cube is:

`rho_2=m_2/(8x^3)`

Next, consider the material used to make the cubes.

Since the two cubes use the same metals, then, the cubes have the same density.

`rho_1=rho_2`

So, to solve for m2, plug-in the density of the two cubes.

`1/x^3=m_2/(8x^3)`

Then, isolate the m2.

`8x^3*(1/x^3)=m_2/(8x^3)*8x^3`

`8=m_2`

Hence, 8 kilograms of metal are needed to make the second cube.

see you actually  can answer this without any calculation.

weight of metal required to form a cube with edge x is =y

if we form a cube with edge 2x ,the new cube will have volume as = 8 cube of edge x.

or we can say we can form a cube of edge 2x by adding 8 cubes of edge x as shown in figure.

so the weight of metal required to form a cube of edge 2x =8y

so weight will be 8 times as of weight of metal required to form the original cube. 

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)
rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

Posted on

You will need to use the density formula, D=M/V, to solve this problem. You are given the mass of the first cube, 1 kg, and volume is represented by x^3.

D=1/x^3

For the second cube, the sides are twice as long, which will effect the volume. Replace x in the volume formula with 2x. This makes your volume (2x)^3 which simplifies to 8x^3.

D2=M2/8x^3

You are told the cubes are made of the same metal, which means they will have the same density. This means you can set your equations equal to each other and solve for mass.

1/x^3=M2/8x^3

8x^3(1/x^3)=M2

8=M2

You will need 8 kg for cube 2.

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

It takes one kilogram of metal to make a certain solid cube. Let the length of the cube's side be L. The volume of the cube is L^3.

A cube with edge twice as long as the first has a volume given by (2*L)^3 = 8*L^3.

The mass of metal required to make a cube is proportional to the volume of the cube. As one kilogram of metal is used to make the first cube, 8 kg of metal is required to make the cube with the longer edge.

We’ve answered 318,929 questions. We can answer yours, too.

Ask a question