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

Area of solids

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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

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



  • 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
  • What is the formula of Area of a cube?

    l3
    4l
    l2
    2l
  • What is the formula of a volume of cuboid ?

    l + b + h
    l × b × h
    2(l × b × h)
    2l × b × h
  • What is the formula of a volume of cube?

    l3
    l2
    l4
    l6
  • If the area of base = 104 cm2 and h = 5.5 cm, then what will be the volume of a cuboid.

    572 cm3
    582 cm3
    537 cm3
    563 cm3
  • What is the formula of surface area of a cube?

    6l2
    6l + b
    l2
    6l
  • If l = 5cm then what will be volume of cube.

    75 cm2
    165 cm2
    125 cm2
    145 cm2
  • Find the surface area of a cube. where h = 4.5 cm.

    143.5 cm2
    134.5 cm2
    123.5 cm3
    121.5 cm2
  • If the surface area of a cubical block is 96 cm2 , what will be its volume?

    64 cm2
    65 cm2
    66 cm2
    63 cm2
  • A rectangular block is 18 cm long, 12 cm broad and 8 cm thick. What ill be its surface area.

    934 cm2
    927 cm2
    912 cm2
    9432
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exact formula to calculate area of hollow and lifeless cuboid

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