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Solid shapes are there dimensional. Solids can be described in various types. Some have a flat surface, some have curved surface and some have both flat and curved surface.
A pattern that you can cut and fold to make a model of a solid shape are a net of a solid figure.
A cube is an object which looks like solid box-shaped that has six identical square faces.
A cube is a special case of a cuboid in which all six faces are squares i. e. lenght = breadth = height
Let each side of cube be a units
Then, total surface area of a cube =2(lb+lh+bh)
= 2(a x a + a x a + a x a)
= 2(a^{2} +a^{2} +a^{2})
= 2 x 3a^{2}
= 6a^{2}
= 6(side)^{2}
Similarly, lateral surface area of a cube = 2h(l +b)
= 2a(a +a)
= 2a x 2a
= 4a^{2}
= 4(side)^{2}
and volume of a cube = l x b x h
= a x a x a
= a^{3}
= (side)^{3}
Cuboid is a solid figure bounded by six faces. A cuboid has 6 rectangular faces. The opposite rectangular plane surfaces are identical. So, it is also called rectangular prism.
The surface of a cuboid consists of six faces which are rectangular in shape. We can categories them in pairs of opposite faces as follows:
Let l, b and h represent the length, breadth and height of the cuboid respectively. To calculate the surface area of the cuboid we need to first calculate the area of each face and then add up all the areas to get the total surface area.
Total area of top and bottom surfaces is lb + lb =2lb
Total area in front and back surfaces is lh + lh = 2lh
Total area of two side surface is bh + bh =2bh
Thus, total surface area of cuboid = 2lb+2lh+2bh
=2(lb + lh +bh)
The lateral surface area of a cuboid includes a front face, back face, and two side faces.
Therefore, lateral surface is of a cuboid = 2lh + 2bh
= 2h(l+b)
Also, volume of a cuboid = l x b x h
A cylinder has two circular plane surfaces, one at its base and another at its top. It has a curved surface in the middle.
To find the surface area of the cylinder, add the surface area of each end plus the surface area of the side. Each end is the circle so the surface area of each end isπr^{2}, where r is the radius of the end.
There are two ends so their combined surface area is 2πr^{2}. The surface area of the side is the circumference times the height or 2πr x h where r is the radius of the end and h is the height of the cylinder.
Therefore, curved surface area = 2πrh
and total surface area = 2πr^{2} = 2πrh = 2πr(r+h)
The base of a cylinder is a circle, with area πr^{2}
The volume of a cylinder is, therefore,
πr^{2} x height = πr^{2}h
A cone is a closed figure with a plane surface and a curved surface.
There are three different solids that you can make with triangles. Mathematicians use the word tetrahedron to describe a triangular pyramid. Since it uses squares as well as triangles.
Tetrahedron is a triangular pyramid having congruent equilateral triangular for each of its faces.
The total surface area of a tetrahedron
= 4 x area of an equilateral triangle
= 4 x \(\frac{√3}{4}\) side^{2}
=√3 side^{2}
Volume of a tetrahedron = \(\frac{1}{3}\) area of base x height of pyramid
Net of tetrahedron
A square pyramid is a pyramid having a square base.
In the figure, ABCD is a square base PO is the height of the pyramid. M is the mid-point of BC.
PM is the slant height of the pyramid.
Lateral surface area of a square pyramid = area of triangular faces
= 4 x area of Δ PBC
= 4 X \(\frac{1}{2}\) x BC X PM
= 2 X BC X PM
Total surface area of the square pyramid = LSA + area of base.
Also, volume of the square pyramid = \(\frac{1}{3}\) area of base x height
= \(\frac{1}{3}\) A x h
Net of square pyramid
Rectangular based pyramid
Tetrahedron
Cylinder
Pentagonal based pyramid
Triangular prism
Tetrahedron
Net of Cube
Net of cylinder
Net of cuboid
Net of cone
Net ofTriangular pyramid
A rectangular block 8cm high has a square base of area 100cm^{2}. Find its total surface area.
The surface area of a cube is 726cm^{2}, find the volume of the cube.
Find the volume and total surface area of a cuboid whose length is 12cm, breadth is 10cm and height is 8cm.
The height of a room is 3.5m and its contains 70m^{3} of air. Find the area of carpet required to cover its floor.
A rectangular block has a square base of area 900cm^{2}. If its total surface area is 3600cm^{2}, find its height.
A room is 10m long, 6m wide and 5m high. Find the cost of painting its four walls at Rs 5 per square meter.
The total Surface area of a cube is 216cm^{2}. Find its volume.
Find the length of each edge of a cube, if its volume is: 125cm^{3}.
A room is 12m long, 8m wide and 5m high. What will be the cost of painting its four walls at Rs 10 per m^{2}.
Find the volume and total surface area of a cube whose each edge is, 6cm.
The total surface area of a cube is 150 m^{2}. Find its volume.
The volume of cuboid is 3456cm^{3}. If the length and breadth of the cuboid are 24cm and 18cm respectively, find its breadth
Find the surface area of a box opened from the top whose shape is like a cube of edge 20cm.
Find the length of each edge of a cube, if its volume is, 512cm^{3}.
How many bricks are required to build a wall 20m long, 2.5m high and 25cm thick if one brick measures 20cm long, 10cm wide and 5cm thick?
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Anmol
Net of rectangle based pyramid
Mar 04, 2017
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Horizonkc
The breaks is 5cm by 3cm by and 2cm and the box is 22cm by 16 cm and 14cm. How many bricks can be kept in the box. Find in six ways.
Mar 03, 2017
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Dima
Find thearea of shaded part of circle
Jan 02, 2017
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