# If each edge of cube is doubled,

1. how many times will its surface area increase?

2. how many times will its volume increase?

Answer

Verified

328.5k+ views

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.

Last updated date: 31st May 2023

â€¢

Total views: 328.5k

â€¢

Views today: 8.85k

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?