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1. how many times will its surface area increase?

2. how many times will its volume increase?

Answer
Verified

Hint: It is given in question that if the edge is doubled then find how many times the surface area and volume increases. For that, take the original cube with edge $a$and find its surface area and volume. Then doubled the edge of the original cube i.e. the edge becomes $2a$. Then compare the original cube and new cube and see how many times its surface area and volume increases.

Complete step-by-step answer:

So the cube is a symmetrical three-dimensional shape, either solid or hollow, contained by six equal squares. The cube is the only regular hexahedron and is one of the five Platonic solids. It has $6$faces, $12$ edges, and $8$ vertices.

The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.

The cube is dual to the octahedron. It has cubical or octahedral symmetry.

The cube is the only convex polyhedron whose faces are all squares.

Cube has its length, breadth and height equal to each other.

The Cube has all its faces in a square shape. In a cube all the faces or sides have equal dimensions.

The plane angles of the cube are the right angle. Each of the faces meets the other four faces.

Each of the vertices meets the three faces and three edges. The edges opposite to each other are parallel.

A cube has eleven nets: that is, there are eleven ways to flatten a hollow cube by cutting seven edges. To color the cube so that no two adjacent faces have the same color, one would need at least three colors.

The cube is the cell of the only regular tiling of three-dimensional Euclidean space. It is also unique among the Platonic solids in having faces with an even number of sides and, consequently, it is the only member of that group that is a zonohedron (every face has point symmetry).

The cube can be cut into six identical square pyramids. If these square pyramids are then attached to the faces of a second cube, a rhombic dodecahedron is obtained (with pairs of coplanar triangles combined into rhombic faces).

Now let us consider a cube with edge$a$.

Therefore, surface area of original cube$=6{{(edge)}^{2}}=6{{a}^{2}}$

Volume of original cube$={{(edge)}^{3}}={{a}^{3}}$

So according to the question, if we doubled the edge of the cube i.e. $2a$.

So, surface area of new cube$=6{{(edge)}^{2}}=6{{(2a)}^{2}}=24{{a}^{2}}$

Also, volume of new cube$={{(edge)}^{3}}={{(2a)}^{3}}=8{{a}^{3}}$

So if the edge of the original cube is doubled the surface area and volume of the new cube is $4$ and $8$times the original cube respectively.

Note: Read the question carefully. Also, do not jumble yourself while simplifying. Do not make any silly mistakes. Avoid the mistake. Your concept regarding the cube should be cleared. Also, you must know the formula for surface area and volume.

Complete step-by-step answer:

So the cube is a symmetrical three-dimensional shape, either solid or hollow, contained by six equal squares. The cube is the only regular hexahedron and is one of the five Platonic solids. It has $6$faces, $12$ edges, and $8$ vertices.

The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.

The cube is dual to the octahedron. It has cubical or octahedral symmetry.

The cube is the only convex polyhedron whose faces are all squares.

Cube has its length, breadth and height equal to each other.

The Cube has all its faces in a square shape. In a cube all the faces or sides have equal dimensions.

The plane angles of the cube are the right angle. Each of the faces meets the other four faces.

Each of the vertices meets the three faces and three edges. The edges opposite to each other are parallel.

A cube has eleven nets: that is, there are eleven ways to flatten a hollow cube by cutting seven edges. To color the cube so that no two adjacent faces have the same color, one would need at least three colors.

The cube is the cell of the only regular tiling of three-dimensional Euclidean space. It is also unique among the Platonic solids in having faces with an even number of sides and, consequently, it is the only member of that group that is a zonohedron (every face has point symmetry).

The cube can be cut into six identical square pyramids. If these square pyramids are then attached to the faces of a second cube, a rhombic dodecahedron is obtained (with pairs of coplanar triangles combined into rhombic faces).

Now let us consider a cube with edge$a$.

Therefore, surface area of original cube$=6{{(edge)}^{2}}=6{{a}^{2}}$

Volume of original cube$={{(edge)}^{3}}={{a}^{3}}$

So according to the question, if we doubled the edge of the cube i.e. $2a$.

So, surface area of new cube$=6{{(edge)}^{2}}=6{{(2a)}^{2}}=24{{a}^{2}}$

Also, volume of new cube$={{(edge)}^{3}}={{(2a)}^{3}}=8{{a}^{3}}$

So if the edge of the original cube is doubled the surface area and volume of the new cube is $4$ and $8$times the original cube respectively.

Note: Read the question carefully. Also, do not jumble yourself while simplifying. Do not make any silly mistakes. Avoid the mistake. Your concept regarding the cube should be cleared. Also, you must know the formula for surface area and volume.

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