## Area of solids

Subject: Compulsory Maths

#### Overview

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

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

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.
##### Understand the formula for calculating the surface area and Volume

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

l= $\frac{96}{6}$ 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.