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Area of solids

Subject: Compulsory Maths

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Some an example of solids is like , Cube , cuboid , sphere , cone , pyramid , etc. Length , breadth, and height are three dimensions of solid objects .This note gives information about the volume and area of a cuboid and another solid figure also .
Area of solids

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

Source : www.ducksters.com Fig :Area of cude
Source : www.ducksters.com
Fig :Area of cude

A cube has 6 square faces . Each square face has an area of l2.

\(\therefore\) Surface area of cube =6l2.

  • A lidless rectangular box does not have its top face .

So , it has only 5 rectangular faces .

\(\therefore\) Area of a lidless rectangular box = 2(lb+bh+lh)-lb

  • A hollow rectangular box does not have top and bottom faces .

So , it has only 4 rectangular faces.

\(\therefore\) Area of hollow rectangular box = 2(lb+bh+lh)-2lb=2(bh +lh)

  • Area of lidless cubical box =5l2.
  • Area of hollow cubical box =4l2

Area of cuboid

Source : www.kidspot.com Fig : Cuboid
Source :www.kidspot.com
 Fig : 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(mm2) , cu.m (m3) , cu.cm(cm3) etc.

  • Volume of cube

\(\therefore\) Volume of cube = l x bx h

  • Volumne of cuboid

\(\therefore\) Volumn of cuboid = Area of base x height

Things to remember
  • A cube has 6 square faces .
  • Area of a lidless rectangular box = 2(lb+bh+lh)-lb
  • Area of hollow cubical box =4l2
  •  Volume of cube = l x bx h
  •  Volume of cube = l x bx h
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
  • It is a network of social relationships which cannot see or touched.
  • common interests and common objectives are not necessary for society.
Videos for Area of solids
Surface Area of Composite Solids
Understand the formula for calculating the surface area and Volume
Questions and Answers

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) cm2

 = 2 (216 + 96 + 144) cm2 = 912 cm2.

Solution:

Here, volume of the box (V) = 1600 cm3

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 cm2

So, its base (b) covers an area of 320 cm2 on the table.

Solution:

Here, the surface area of the cubical block = 96 cm3

 or, 6l2 = 96 cm2

l2 = \(\frac{96}{6}\) cm2 = 16 cm2

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 cm3

or, l×b×h = 768 cm3

or, 2x × x × 6 cm = 768 cm3

or, 2x2 = \(\frac{768}{6}\) cm2 = 128 cm2

or, x2 = \(\frac{128}{2}\) cm2 = 64 cm2

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) cm2 

 = 2 (128 + 48 + 96) cm2 = 544 cm2 ans.

A cuboid has the 6 rectangular faces. Its surface area is the total sum of the area of 6 rectangular faces. Its formulae is:

Surface area of cuboid =2lb + 2bh + 2lh = 2 (lb + bh + lh)

A cube has 6 square faces. Each square face has area of l2.

Surface area of a cube = 6l2.

Quiz

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