Chapters
We all have seen a rectangle at this point. Four sides, parallel sides are the same, length and width, and that is it. At that time we were working in a two-dimensional surrounding, let's twist things up. Think about it, how a rectangle would look like if we consider the third dimension too? Let's talk about it.
What is a Cuboid?
We all receive parcels, from loved ones or maybe you ordered something. Usually, they come in the packaging, which is, in a cardboard box. If the dimension of that box is not uniform then the card box will be called Cuboid.
In simple words, a cuboid is a parallelepiped that has all rectangular faces joined at right angles. Basically, it is a three-dimensional geometrical shape that has six faces, twelve edges, and eight vertices. Cube and cuboids are two different shapes, don't get confused. The identification of a cube is that it has different dimensions. Like rectangles, the opposite sides will be equal.
Unfold of a Cuboid
Unfolding three-dimensional shapes isn't only fun but it is another way to understand this complex geometry. For further study of cuboids, let's unfold this figure.
The above image is the image of an unfolded cuboid. As you can see, the cuboid is made up of rectangles. The colours represent rectangles having the same dimensions. For example, red colour rectangles are the top and bottom of the cuboid. The green colour rectangles are the front and behind side view of the cuboid. Last but not least, the while colour rectangles are the side views of the cuboid.
Diagonal of a Cuboid
Surface Area of a Cuboid
The surface area of a cuboid means the space occupied by the surface of the cuboid. This is where the knowledge of the unfolding of cuboids comes in. In short, the area occupied by the unfolded cuboid is the surface area.
$A = 2(ab + ac + bc)$
Where,
a, b, and c are the length, width, and height of the cuboid.
Volume of a Cuboid
The volume of a cuboid means the space occupied by the total cuboid. The surface area is the calculation of the area of the surface but the volume is the calculation of the total space inside of the cuboid.
$V = a times b times c$
Examples
Calculate the diagonal of a cuboid with a length of 10 cm, a width of 4 cm and a height of 5 cm.
Calculate the volume (in cubic centimetres) of a room that is 5 m long, 40 cm wide and 2,500 mm high.
$l = 5m, quad w = 40cm = 4m, quad h = 2500mm = 2.5m$
$V = a times b times c$
$V = 5 times 4 times 2.5$
$V = 50 { m }^{ 3 } = 50,000,000 { cm }^{ 3 }$
A swimming pool is 8 m long, 6 m wide and 1.5 m deep. The water-resistant paint needed for the pool costs 6 dollars per square meter.
1 How much will it cost to paint the interior surface of the pool?
2 How many litres of water will be needed to fill it?
$A = ab + 2(ac + bc)$
$A = 8 times 6 + 2(8 times 1.5) + 2 (6 times 1.5) = 90 { m }^{ 2 }$
$90 { m }^{ 2 } times 6 frac { $ }{ { m }^{ 2 } } = 540$
$V = 8 times 6 times 1.5 = 72 { m }^{ 2 } times 1000 = 72,000 l$
A moving company is trying to store boxes in a storage room with a length of 5 m, a width of 3 m and a height of 2 m. How many boxes can fit in this space if each is 10 cm long, 6 cm wide and 4 cm high?
$l = 5m quad { l }_{ 1 } = 1 m$
$w = 3 m quad { w }_{ 1 } = 0.6 m$
$h = 2m quad { h }_{ 1 } = 0.4 m$
$V = 5 times 3 times 2 = 30 { m }^{ 3 }$
${ V }_{ 1 } = 1 times 0.6 times 0.4 = 0.24 { m }^{ 3 }$
No. of boxes = $frac { 30 }{ 0.24 } = 125$
How many square tiles (20 cm x 20 cm) are needed to cover the sides and base of a pool which is 10 m long, 6 meters wide and 3 m deep?
$A = 10 times 6 + 2 (10 times 3) + 2 (6 times 3) = 156 { m }^{ 2 }$
${ A }_{ square } = 20 times 20 = 400 { cm }^{ 2 } : 10,000 = 0.04 { m }^{ 2 }$
No. of tiles = $frac { 156 }{ 0.04 } = 3,900$
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Hello,
the solution of Exercise No.3 …volume 1 = 30m3
and the last fraction is 30/0.24 = 125