Subject: Compulsory Maths

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}.

- 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 =5l
^{2}. - Area of hollow cubical box =4l
^{2}

**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.

**Volume of cube**

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

**Volumne of cuboid**

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

- A cube has 6 square faces .
- Area of a lidless rectangular box = 2(lb+bh+lh)-lb
- Area of hollow cubical box =4l
^{2} ^{ 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.

A rectangular block is 18 cm long, 12 cm broad and 8 cm thick. Find its surface area.

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}.

The volume of a rectangular box is 1600 cm^{3} and its height is 5 cm. If it is placed on a table, find the area covered by it on the table.

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.

If the surface area of a cubical block is 96 cm^{3}, find the length of its each edge.

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

A cuboid is twice as long as its breadth and it is 6 cm high. If its volume is 768 cm^{2}.

- Find the length and breadth.
- Find its surface area.

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.

Define the area of Cuboid. Mention its formulae.

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)

Define the area of a cube. Mention its formule.

A cube has 6 square faces. Each square face has area of l^{2}.

Surface area of a cube = 6l^{2}.

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