Question

A metal cube of edge 12cm is metalled and casted into three small cubes . Tf the edge of two small cubes be 6 cm and 8cm then the adge of the third small is

Answer 1

ANSWER

The edge of the third smaller cube is 10 m.

Explanation :-

Given:

We are given with following measures:

a metal cube of edge 12cm

two small cubes with edges 6cm and 8cm.

Let's consider the metal cube as a bigger cube which is represented with letter R and measuring edge=12 cm.

And two smaller cubes as edges of first first one representing with r¹ measuring 6 cm and and edge of the second one representing with r² measuring as 8cm.

So,

edge of the bigger cube (R) = 12cm

Edge of r¹ = 6cm

Edge of r² = 8cm

We will first find the volume of the bigger cube with edge 12 cm

Formula to be used for finding the volume:

Volume of the cube = (Edge)³

Let's apply the formula to find the volume of the bigger cube.

Volume of the bigger cube=(Edge)³

Volume of the bigger cube = (12)³

Volume of the bigger cube= 144×12

Volume of the bigger cube = 1728m³

We now have the volume of the bigger cube which is melted and formed into three smaller cubes which means the volume of this bigger cube is equal to the volume of the smaller cubes.

So, now we will need to find the volume of the r¹ cube and r² cube

Volume of r¹ = (edge)³

Volume of r¹ = (6)³

Volume of r¹ = 36×6

Volume of r¹= 216 m³

Now we will calculate the volume of r²

Volume of r²= (edge)³

Volume of r²= (8)³

Volume of r²= 64×8

Volume of r²= 512m³

Now, we have the volume of bigger cube, r¹ and r².

We will therefore now calculate the total volume of all these three cubes together.

Total Volume = volume of r¹ + volume of r² + volume of r³.

V = r¹+ r²+r³

1728 = 216+ 512+r³

1728= 728+r³

1728-728=r³

1000= r³

Volume of r³ = 1000m³

We have the volume of the third cube and we are asked to find the edge of the cube, so,

(Edge)^3= 1000

Edge = ³√1000

Edge = ³√10×10×10

Edge = 10 m

Hence, the edge of the third cube = 10m.

Answer 2

Answer:

10 cm

Step-by-step explanation:

Edge of a bigger cube (R)= 12 m

Edge of a first smaller cube(r²)= 8 m

Edge of a second smaller cube(r²)= 6m

Volume of a cube = side³

Volume of a bigger cube(V) = (sides)³

= (12)³= 1728m³

It is melted into three other cubes ,so the volume of the smaller cubes remains same as the volume of bigger cube .

volume of the first smaller cubes(V1)= (8)³=512m³

volume of second smaller cube(V2) = 6³ = 216m³

Total volume(V) = volume of first smaller cube(V1) + volume of second smaller cube(V2)+ + volume of third smaller cube(V3)

V= V1+V2+V3

1728 = 512 +216+V3

1728 = 728+V3

1728 - 728 = V3

1000 = V3

volume of third cube = 1000 m³

Edge³= 1000

Edge = ³√1000

Edge =³√10×10×10

Edge= 10 m

Hence, the edge of the third cube is = 10 m