Question

If side of the cube is increased by 300% then its surface area will increase by ________.

Answer 1

The surface area of the cube will increase by 96 times.

If the side of a cube is increased by 300%, then its length will be 4 times as long as the original side length (1 + 3 = 4).

Since the surface area of a cube is given by 6 * (side length)^2, when the side length is increased by 300%,

then surface area will increase by  $6 * 4^2 = 6 * 16 = 96$ times the original surface area.

So the surface area of the cube will increase by 96 times.

• The surface area of a 3-dimensional object is the total area of all of its exposed faces, or surfaces.

• It is a measure of how much area is covered by the object, and it is typically measured in square units. For example, the surface area of a cube would be the sum of the areas of its six faces

• Surface area is an important concept in geometry and physics. In geometry, it is used to calculate the area of the surface of various shapes such as cubes, spheres, cylinders, and cones. In physics, it is used to calculate the heat transfer, fluid flow, and other properties of objects.

• Surface area is also an important concept in engineering, particularly in the fields of architecture, mechanical engineering, and aerospace engineering where it is used to calculate the amount of material needed to construct an object or the aerodynamic properties of an object.

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Answer 2

Surface area:  In the geometry we need to calculate the surface area of various type of shapes. Every shapes have different type of surface like cube have rectangular surface, sphere have circle surface etc.

Cube: In the geometry the cube is whose have 6 surface,8 vertex and 12 sides. whose shape have all the criteria mention above is called the cube.

As per question we need to find the cube surface area how much increase.

The given information is the cube is increased by 300%.

The cube sides increased by 300% then the length will be 4 times of the original length.

we know that the area of surfaces of a cube is

=6*$a^{2}$, here a= length of the cube side.

Now the side of the cube is 4a.

The surface area will be increase = 6*$(4a)^{2}$

                                                          = 96$a^{2}$.

So the surface area will increase 96 times.

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