Some example of solids is like , Cube , cuboid , sphere , cone , pyramid , etc. Length , breadth, and height are three dimensions of solid objects .
Area of cube
A cube has 6 square faces . Each square face has an area of l^{2}.
\(\therefore\) Surface area of cube =6l^{2}.
So , it has only 5 rectangular faces .
\(\therefore\) Area of a lidless rectangular box = 2(lb+bh+lh)-lb
So , it has only 4 rectangular faces.
\(\therefore\) Area of hollow rectangular box = 2(lb+bh+lh)-2lb=2(bh +lh)
Area of cuboid
Area of top and bottom faces = lb+lb=2lb
Area of side faces = bh +bh =2bh
Area of front and back faces = lh + lh=2lh
\(\therefore\) Surface area of cuboid = 2lb+2bh+2lh =2(lb+bh+lh)
Volume of solids
The total space occupied by a solid is called its volume . Volume is measured in cu.mm(mm^{2}) , cu.m (m^{3}) , cu.cm(cm^{3}) etc.
\(\therefore\) Volume of cube = l x bx h
\(\therefore\) Volumn of cuboid = Area of base x height
Solution:
Here, length of the block (l) = 18 cm
breadth of the block (b) = 12 cm
thickness of the block (h) = 8 cm
Now, the surface area of the block = 2 (l×b + b×h + l×h)
= 2 (18×12 + 12×8 + 18×8) cm^{2}
= 2 (216 + 96 + 144) cm^{2} = 912 cm^{2}.
Solution:
Here, volume of the box (V) = 1600 cm^{3}
height of the box = 5 cm
Now, volume of the box = Area of its base × height
\(\therefore\) Area of the base × height = 1600
or, Area of its base × 5 = 1600
or, Area of its base = \(\frac{1600}{5}\) = 320 cm^{2}
So, its base (b) covers an area of 320 cm^{2} on the table.
Solution:
Here, the surface area of the cubical block = 96 cm^{3}
or, 6l^{2} = 96 cm^{2}
l^{2 }= \(\frac{96}{6}\) cm^{2} = 16 cm^{2}
l = \(\sqrt{16 cm^2}\) 4 cm
Solution:
Here, Let the breadth of the cuboid be x cm.
\(\therefore\) The length of the cuboid will be 2x cm.
Now, the volume of the cuboid = 768 cm^{3}
or, l×b×h = 768 cm^{3}
or, 2x × x × 6 cm = 768 cm^{3}
or, 2x^{2} = \(\frac{768}{6}\) cm^{2} = 128 cm^{2}
or, x^{2} = \(\frac{128}{2}\) cm^{2} = 64 cm^{2}
or, x = \(\sqrt{64cm^2}\) = 8 cm
So, the breadth (b) = x = 8 cm and the length (l) = 2x = 2 × 8 cm = 16 cm
Again, surface area of the cuboid = 2 (l×b +b×h + l×h)
= 2 (16×8 + 8×6 + 16×6) cm^{2}
= 2 (128 + 48 + 96) cm^{2} = 544 cm^{2} ans.
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exact formula to calculate area of hollow and lifeless cuboid
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Feb 03, 2017
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