the Length breadth and height of a chocolate boxes are in the ratio 5:4:3 if its volume is 7500 cm cube then find its dimensions​

Question

the Length breadth and height of a chocolate boxes are in the ratio 5:4:3 if its volume is 7500 cm cube then find its dimensions​

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Mary 1 month 2021-08-18T02:40:49+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-18T02:42:11+00:00

    Answer:

    l = 25cm

    b = 20 cm

    h = 15 cm

    Step-by-step explanation:

    volume of rectangle= l* b*h

    5x * 4x * 3x = 7500

    60x³ = 7500

    x³ = 7500/60

    x³ = 125

    x = 5

    l = 5*5 = 25

    b = 4*5 = 20

    h = 3*5 = 15

    0
    2021-08-18T02:42:14+00:00
    • The length of a chocolate box = 25 m.
    • The breadth of a chocolate box = 20 m.
    • The height of a chocolate box = 15 m.

    Given :

    • The ratio of the length, the breadth and the height of a chocolate box = 5 : 4 : 3.
    • The volume of a chocolate box = 7500 cm³.

    To Find :

    • The dimensions of a chocolate box.

    Solution :

    Let,

    The length of a chocolate box be 5x.

    The breadth of a chocolate box be 4x.

    The height of a chocolate box be 3x.

    First, we need to find the value of x.

    Given,

    Volume of a chocolate box = 7500 cm³

    We know that,

    Volume of a chocolate box = length × breadth × height

    That means,

    length × breadth × height = 7500 cm³

     \rm\implies 5x \times 4x \times 3x = 7500  \: {cm}^{3}  \\  \\ \rm \implies 5x \times  {12x}^{2}  = 7500 {cm}^{3}  \\  \\ \rm\implies 60 {x}^{3}  = 7500 \:  {cm}^{3}  \\  \\ \rm\implies   {x}^{3} =   \frac{750 \cancel0 \:  {cm}^{3} }{6 \cancel0}  \\  \\ \rm \implies  {x}^{3}  =  \cancel \dfrac{750}{6} \:  {cm}^{3}   \\  \\ \rm \implies  {x}^{3}  =   \cancel\dfrac{375}{3}  \:  {cm}^{3}  \\  \\ \rm \implies  {x}^{3}  = 125 \:  {cm}^{3}  \\  \\  \rm \implies  {x}=  \sqrt[3]{125 \:  {cm}^{3} }  \\  \\  \rm \implies x = 5 \: cm

    Hence, the value of x is 5 cm.

    So, the dimensions of a chocolate box are :

    The length of a chocolate box = 5x = 5 × 5 cm = 25 cm.

    The breadth of a chocolate box = 4x = 4 × 5 cm = 20 cm.

    The height of a chocolate box = 3x = 3 × 5 cm = 15 cm.

    Hence,

    The dimensions of a chocolate box are 25 cm, 20 cm and 15 cm.

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