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A Cuboidal Contains 189 Cm3 Wood. If It Be 7cm Long And 4.5cm High, Find Its Breadth

A cuboidal wooden block contains 189 cm3 wood. If it be 7cm long and 4.5cm high, find its breadth.

Answer

The solid sides of a rectangle are cuboids. Cuboid is a shape of three-dimensional or shape of polyhedron. Cuboids consist of six rectangular shaped sides or edges, which are called faces of the cuboids. Cuboid consists of 12 edges and 8 vertices. All the faces are rectangle in shape and the corners of the cuboid are vertices. These vertices are 90 degree in angle. It is a closed geometric figure, which is three-dimensional and it is bounded by a region, which consist of six rectangular planes.

Cuboid

A cuboid is consists of six rectangles. Each rectangle is known as face of thee cuboid. In the above figure, there six faces of the cuboid. ABCD, ADHE, AEFB, DHGC, CGFB, HEFG these are the six faces of the above cuboid. The top face, which is ABCD and the bottom face, which is HEFG both construct a couple of opposite faces. In the same way, AEFB, DHGC, ADHE, CGFB these faces construct opposite face’s pair. Any two faces except the opposite faces are known as adjacent faces. It is consider that ABCD is a face, which is adjacent to AEFB, CGFB, DHGC and ADHE.

The edges or the sides of the cuboid are the line segment within the two vertices adjacent. Twelve edges are there in the cuboid. AB, AD, AE, EH, EF, DH, DC, GH, GC, GF, BF, BC these are the faces of the cuboid and the opposite edges are equal of the rectangle.

Hence, CD=AB=HG=FE, BF=AE=DH and AD=FG=EH=CB.

Any one face of the cuboid is known as base of the cuboid. There are four faces of the cuboid. These are adjacent to the base. These faces in the cuboid are called lateral faces. The surface is known as base of solid on which the solid rests. HEFG is the base of the above cuboid.

The point, where the three edges intersect is called the vertex of the cuboid. A cuboid consists of eight vertices. A, B, C, D, E, F, G and H are representing the vertices of the cuboid in the above figure. The twelve edges or the sides are grouped in three groups. In one group all, the edges are equal. Therefore, there are there different groups such as length, height and breadth.

The area of the surfaces of the cuboid is equal to areas of the cuboid of the rectangle faces. If it is, consider to have length as l cm, breadth as b cm and height as h cm,

The area of the face ABCD = the area of the face EFGH = (l*b) cm^{2}

The area of the face AEHD = the area of the face BFGC = (b*h) cm^{2}

The area of the face ABFE = the area of the face DHGC = (l*h) cm^{2}

The total area of the surface of the cuboid = the sum of areas of all the six rectangle faces

= 2 (lb + bh + lh)

Cuboid includes polyhedron or flat faces and straight edge. Sometimes the cuboid is called rectangular polyhedron as all the faces are in rectangular shape. Cuboid consists of six equal faces. The adjacent faces are different in lengths but the opposite faces of the cuboid are congruent. Three faces of the cuboid construct the eight vertices of the cuboid. The cuboid is also known as hexahedron. The hexahedron consists of three shapes of dimensional with the six faces of the cuboid. In the cuboid, every face is rectangle in shape and the vertices or the corners are 90 degree in angle. The opposite faces of the cuboid are equal.

Let, the length is l, breadth is b and the height is h.

Four side faces area = 2 (b*l) = 2 (h*b) = 2 (b*l) * h = height * base perimeter.

The area of the side faces of four sides are known as lateral surface of the area of the cuboid.

Therefore, the total surface area = 2 (l*h) + (h*b) + (l*b)

Volume of the cuboid = height * breadth * length

Volume of the cuboid (v) = h * b * l

The longest diagonal length of the cuboid = √ (h^{2} + b^{2} + l^{2}).

Any closed box made of three couple of rectangle faces of the cuboid, which is placed at opposite side of each other. It is joined at the angles, those are right angle. It is also called rectangle parallelepiped. The cuboid is a right prism. It is a unique case of parallelepiped and it is corresponding to the parlance, which is called rectangular box. Cuboids are constructed in Wolfram Language as the cuboid. It coordinates with the opposite corners of the cuboid. If the length of the sides of the cuboid is denoted as a, b and c, all the sides or the edges of the cuboids will be equal that is a = b = c. it is known as cube. The length of the integer edge of the cuboid is a > b > c. The space diagonals are integers. The face diagonals are known as Euler brick and the cuboid is known as perfect cuboid.

The volume of cuboid is V = a * b * c

The total surface area of the cuboid is S = 2 (ab + bc + ca).

The face diagonals length of the cuboid are:

d_{ab} = √ a^{2} + b^{2}

d_{bc} = √ b^{2} + c^{2}

d_{ca} = √ c^{2} + a^{2}

The space diagonals length of the cuboid is

d_{abc }= √ a^{2} + b^{2} + c^{2}

The length of the wooden block of the cuboid is = 7 cm

The height of the wooden block of the cuboid is = 4.5 cm

The breadth of the wooden block of the cuboid is = B cm

The volume given for the cuboid block = 189 cm^{3}

L * H * B = 189

7 * 4.5 * B = 189

B = 189 / 31. 5 = 6 CM

Therefore, the breadth of the wooden cuboidal block will be 6 cm.