Question

Surface Are and Volume of a cube and cuboid.....

TOPICS THAT I WANT ARE -----

-- Ïñtrōdúçtîõñ

-- Cuboid and Cube

-- Terms related to Cuboid

-- Total surface Area of a Cuboid and a cube

-- Basic conversion units

-- ãñy twô èxâmplê

Answer 1

hello!

Volume---> The space occupied by a solid Is known as its volume.
Total surface area---> The total area of the solid boly is called its Total surface area.

Cuboid---> A solid bounded by six rectangular plane faces is called a cuboid
Cube---> A cuboid whose length, breadth and height are all equal is called a cube.

Terms related to cuboid--->
(i)faces:6 rectangular faces
(ii)edges:12 edges
(iii)vertices:8 vertices
Any face of the cuboid is called its base.
The 4 faces which meet the base are called the lateral faces if the cuboid.

Total Surface Area of a Cuboid--->
2 (lb+bh+lh)sq units [where l=length, b=breadth, h=height]
Total Surface Area of a Cube--->(6a^2)sq units [where a=edge]

Basic Conversion units--->
1cm^3=1000mm^3=1ml
1dm^3=1000cm^3=1l
1m^3=1000dm^3=1000l
1l=1dm^3=1000cm^3=1000ml
1kl=1000l

1st example--->
the dimensions of a cuboid are: length=8m, breadth=6m, height= 3.5m . Find its Total surface area
Total surface area=2 {8×6+6×3.5+8×3.5}m^2
=194m^2
2nd example--->Find the total surface area of a cube each of whose sides measures 8cm.
Length of each side=8cm
Total surface area=(6×8×8)cm^2
=384cm^2

hope it helps... :)

Answer 2

hello...

SURFACE AREA AND VOLUME OF A CUBE AND CUBOID

⛔ INTRODUCTION

The plain figures like triangle, quadrilateral, polygon, circle etc are Drawn on plane like notebook or blackboard are said to be dimensional figured where as the solid figures like box, cylinder, cone, sphere etc cannot be drawn accurately on a two dimensional plane for they have height ( in addition to length and breadth ) and so are called three dimensional figures.

↪️ CUBOID AND CUBE

CUBOID ➡️A CUBOID IS A SOLID FIQURE BOUNDED BY SIX RECTANGULAR REGIONS

EXAMPLE ➡️A BOOK, A MATCHBOX, AN ICE CREAM BRICK, A TILE, A CHALK BOX, ETC.,

✳️ SOME TERMS RELATED TO CUBOID

☢️ FACE :- each rectangular plain region of the cuboid is called face a cuboid has 6 faces

EXAMPLE :- in a cuboidal rom for walls are known as lateral faces

☢️ EDGE :- every pair of adjacent faces meet in a line segment and this line segment is called an edge of the cuboid the keyboard has 12 edges

☢️ VERTEX :- the point where three adjacent edges made is what is the vertex a cuboid has 8 vertices

☸️ CUBE :- a cuboid whose Length breadth and height are all equal is called cube

EXAMPLE :- a dice, an ice cube, a sugar cube, etc.

✡️ TOTAL SURFACE AREA (SURFACE AREA) OF A CUBOID AND A CUBE

The sum of the areas of all six faces (rectangular region) is called it's surface area.

Also, the opposite faces are equal in areas.

l, b, and h be the length, breadth and height of a Cuboid. then.,

1.) Surface area of Cuboid = 2(lb+bh+hl)

2.) Surface area of cube = 6l²

where l is the length of one edge of a cube

3.) Lateral surface area of Cuboid = 2 (l+b)h

4.) lateral surface area of cube = 4l²

5.) surface area of an open box ( box without lid ) = 2(lb+bh+hl)-lb or 2(l+b)h

6.) the length of the diagonal of a cuboid = √l²+b²+h² ( underoot starts from l till end of the formula )

7) the length of the diagonal of a cube =

$\sqrt{3} l$

⚛️ CONVERSION OF UNITS

1) 1ml = 1cm³ = 1cm×1cm×1cm = 10mm× 10mm× 10mm = 1000m³

2) 1l = 1000ml

3) 1kl = 1000l

4) 1kl= 1m³ = 1m×1m×1m = 100cm×100cm×100cm= 10^6 cm³

5) 1m³= 10dm³

⚜️ EXAMPLES

1.) dimension of cuboid are in ratio 3:4:5 and its total surface area is 188 metres² find the dimensions.

Ans :- The dimensions of Cuboid 3:4:5

let l = 3x
b = 4x
h = 5x

T.S.A = 188m²

2(3x×4x+4x×5x+5x×3x)=188

(12x²+20x²+15x²)=94

47x² = 94

x² = 94/47=2

x=$\sqrt{2}$
So, l = 3x = 3 × $\sqrt{2}$

=$\sqrt[3]{2}$

b = $\sqrt[4]{2}$

h = $\sqrt[5]{2}$

2.) a small indoor greenhouse is made entirely of Glass panes held together​ with tape it is 30cm long, 25cm wide, 25cm high. Find area of the glass ?

Ans :- Area of glass = T.S.A of the Cuboid

2(30×25+25×25+25×30)

2(750+625+750)cm²

4250cm²

⚜️⚜️ Hope it helps you.. ⚜️⚜️