Notes on Area of solids | Grade 7 > Compulsory Maths > Perimeter, Area and Volume | KULLABS.COM

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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

• 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
.

### Very Short Questions

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.

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• ### What is the formula of surface area of cuboid?

2(lb + bh + lh)
2lb + bh + 2lh
lb + 2bh + lh
(lb + bh + lh)2

l3
4l
l2
2l

l + b + h
l × b × h
2(l × b × h)
2l × b × h

l3
l2
l4
l6

572 cm3
582 cm3
537 cm3
563 cm3

6l2
6l + b
l2
6l

75 cm2
165 cm2
125 cm2
145 cm2

143.5 cm2
134.5 cm2
123.5 cm3
121.5 cm2

64 cm2
65 cm2
66 cm2
63 cm2

934 cm2
927 cm2
912 cm2
9432