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    You are at:Home»Pure Math»Geometry»Volume of cube and cuboid, Area of cube and cuboid | Allmathtricks
    formulas of cuboid and Cube - Surface Area, volume, Diagonal Length, Perimeter with examples | allmathtricks
    Geometry

    Volume of cube and cuboid, Area of cube and cuboid | Allmathtricks

    sivaalluriBy sivaalluriJune 10, 2020Updated:April 2, 2025No Comments6 Mins Read

    This page provides formulas for Surface Area, volume, Diagonal Length, Perimeter of Cuboid and Cube   with examples

    Table of Contents

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    • Surface Area and volume of cuboid and Cube Formulas with Examples
      • Cuboid
      • Cube
        • Perimeter of Cuboid and Cube
        • Surface Area of Cuboid and Cube
        • Volume of Cuboid and Cube
        • The diagonal length of a Cuboid and Cube
        • Examples of Cuboid and Cube

    Surface Area and volume of cuboid and Cube Formulas with Examples

    Cuboid

    A solid that contains length, breadth, and height is called a cuboid. A cuboid is three-dimensional box. It is virtue of its length (l), breadth ( b) and height (h).

    Cube

    A cube is a cuboid that has all its edges equal

    i,e length = breadth = height = a

     

     

     Surface Area and volume of cuboid and Cube Formulas with Examples | Allmathtricks

    A cuboid or cube have 6 faces, 8 vertices and 12 edges.

    Perimeter of Cuboid and Cube

    The perimeter of the cube or cuboid gives the complete edge to edge separation of the shape of the same

    Perimeter of Cuboid = 4 ( l + b + h)

    Perimeter of cube = 4 ( a + a + a ) = 12a

    Surface Area of Cuboid and Cube

    The area of the four faces of a cube or cuboid is called the lateral surface area of the same.

    Lateral Surface area of cuboid = lh + lh + bh + bh = 2 (lh + bh) = 2 (l +b)h

    Lateral Surface area of cube = aa + aa + aa + aa = 4a2

    Six rectangular pieces are covered by cuboid total surface area.

    The total surface area of a cuboid = Total area of all rectangular pieces  = lb + lb + bh + bh + lh + lh

     Area of Cuboid = 2 ( lb + bh + lh)

    Total surface area of cube = Total area of all square pieces  = aa + aa + aa + aa+ aa + aa

     Area of Cube = 6a2

    Volume of Cuboid and Cube

    The cuboid or cube measure of this occupied space is called the volume of Cuboid and Cube.

    The total surface area of a cuboid = The area of the plan rectangle occupied by each rectangle x height = Length x Breadth x Height

     Volume of the Cuboid =( l x b x h) cubic units

    Volume of Cube = edge x edge x edge = a x a x a = a3 cubic units

    The diagonal length of a Cuboid and Cube

    Diagonal a Cuboid (d) =  \sqrt{l^2 + b^2 + h^2}

    Diagonal a Cube (d) =  \sqrt{3a}

     

    Formulas of Cuboid and Cube

     Description  Cuboid  Cube
     Perimeter  4 ( l + b + h)  12a
     Lateral Surface Area  2 (l +b)h  4a2
     Total surface area  2 ( lb + bh + lh)  6a2
     Volume  ( l x b x h)  a3
     Diagonal Length     \sqrt{l^2 + b^2 + h^2}    \sqrt{3a}

    Examples of Cuboid and Cube

    Ex – 1 : The required rectangular box  has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. Then how many Square sheets are required to prepare rectangular box with side of 40 cm.

    Solution: Here, a rectangular box

    Length = l = 80 cm ,

    Breadth = b = 40 cm &

    Height = h = 20 cm

    Side of the square sheet = a = 40 cm

    Total surface area of the rectangular box = 2 (lb + bh + lh ) = 2  [ (80 x 40) + (40 x 20) + (80 x 20)] = 11200 cm2

    The surface area one single square sheet = 2 a2 = 2 x 40 x 40 =1600 cm2

    Therefore, the number of square sheets required to prepare a rectangular box = Total surface area of the rectangular box / Total surface area of the rectangular box

    = 11200 / 1600 = 7

    Hence, 7 sheets are required.

    Ex-2 : The length of a rice godown is double its breadth. Its height is 3 m. The area of four walls is 108 m2. Find the volume of the godown.

    Solution: Take godown breadth = b m  then length = l = 2b m, height = 3 m

    Area of four sides = 2(l+b)h = 108

    ⇒ 2 ( 2b + b) 3 = 108

    ⇒ b = 6 m

    ⇒ l = 2b = 12 m

    Volume of rice godown = 12 x 6 x 3 = 216 m3

    Ex-3 : A solid cube of lead has edge measures 44 cm. How many spherical balls can be made by using a solid cube of lead, and each ball being 88 cm in diameter?

    Solution:

    Side of the solid cube lead = a =  44 cm

    Volume of the solid cube = a3 = 443

    Radius of spherical balls = r = 88/2 = 44 cm

    Volume of each spherical ball =  \frac{4}{3} \pi r^3   = ( 4/3) x (22/7) x (3 x 3 x 3 )

    Number of spherical balls = Volume of the solid cube/Volume of each spherical ball

    = 44 x 44 x 44 x 3 x 7 / ( 4 x 22 x 44)

    = 462 nos.

    Ex-4 : Two cubes volume 64 cm3 each are joined end to end. Find total surface area of the resulting cuboid.

    Solution: Take the side of the cube = a

    Then Volume of cube = a3  = 64 cm3

    ⇒ a = 4 cm

    Now resulting cuboid length =  4 + 4 = 8 cm , breadth = 4  cm & height = 4 cm

    Surface Area of the cuboid = 2 ( 8×4 + 4×4 + 4×8) = 160 cm2

    Ex-5 : The ratio of curved surface area and total surface area of a cube with edge ‘a’ cm is

    Solution: Curved surface area of cube = 4a2

    The total surface area of cube = 6a2

    So the ratio of curved surface area to total surface area of cube = 4 : 6 = 2 : 3

    Ex-6 : Find the diagonal of a cuboid with length = 2a cm, breadth = 3a cm and height =  \sqrt{12} \ a cm

    Solution: Cuboid has length (l), breadth ( b), and height (h).

    then Diagonal a Cuboid (d) =  \sqrt{l^2 + b^2 + h^2}

    =  \sqrt{(2a)^2+(3a)^2+(\sqrt{12} \ a)^2}

    = 5a cm

    Ex-7 : A cubical solid block of metal 49 cm x 44 cm x 18 cm is melted and formed into a solid sphere. Then find the radius of the sphere.

    Solution: Here, Volume of solid block = Volume of solid sphere

    Let the radius of the sphere = r cm

    ⇒ 49 x 44 x 18 = (4/3) x (22/7) x (r3)

    ⇒ r = 21

    Related articles:

    Formulas for arc, Perimeter, Segment of circle

    Formulas of area and perimeter of all two dimensional shapes

    Quadrilateral formula for area and perimeter

    Terminology and Formulas of the Triangles

    Number of triangles in the given figure | How to count number of triangles

    How to find last digit of any number with power

    Area of cube and cuboid cube cuboid Diagonal Length of Cuboid and Cube Perimeter of Cuboid and Cube Surface Area Surface Area of Cuboid and Cube Volume of cube and cuboid
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