Question

the length breadth and height of a cuboid are in the ratio 5 ratio 3 ratio 2 and its total surface area is 3968 CM square find the dimensions of the cuboid​

Answer 1

Answer:

TSA of cuboid = 2(lb + bh + hl)

Let,

L = 5x

B = 3x

H = 2x

2( 5x * 3x + 3x* 2x + 2x * 5x) = 3968

2(15x^2 + 6x^2 + 10x^2) = 3968

2(31x^2) = 3968

62x^2 = 3968

x^2 = 3968/62

x^2 = 64

x = 8

L = 5*8 = 40

B = 3*8 = 24

H = 2*8 = 16

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Answer 2

Answer:

$\bigstar{\bold{Length\:of\:the\:cuboid=40\:cm}}$

$\bigstar{\bold{Breadth\:of\:the\:cuboid=24\:cm}}$

$\bigstar{\bold{Height\:of\:the\:cuboid=16\:cm}}$

Step-by-step explanation:

$\Large{\underline{\sf{Given:}}}$

• Length, breadth and height of a cuboid are in the ratio 5 : 3 : 2
• Total surface area of the cuboid = 3968 cm²

$\Large{\underline{\sf{To\:Find:}}}$

• The dimensions of the cuboid

$\Large{\underline{\sf{Solution:}}}$

➜ Here we have to find the length, breadth and height of the cuboid.

➜ Let us assume the length of the cuboid as 5x cm

➜ Let the breadth of the cuboid as 3x cm

➜ Let the height of the cuboid be 2x cm

➜ The total surface area of a cuboid is given by,

    TSA of a cuboid = 2 (lb + bh + lh)

    where l = length of the cuboid

    b = breadth of the cuboid

    h = height of the cuboid

➜ But by given we know that,

    TSA of cuboid = 3968 cm²

➜ Hence,

    2 (5x × 3x + 3x × 2x + 5x × 2x) = 3968

    2 ( 15x² + 6x² + 10x²) = 3968

    31x² = 1984

       x² = 1984/31

       x² = 64

       x = √64 = 8

➜ Hence the value of x is 8.

➜ Now finding the dimensions,

    Length = 5x = 5 × 8 = 40 cm

➜ Hence length of the cuboid is 40 cm.

    $\boxed{\bold{Length\:of\:the\:cuboid=40\:cm}}$

➜ Breadth = 3x = 3 × 8 = 24 cm

➜ Hence breadth of the cuboid is 24 cm.

    $\boxed{\bold{Breadth\:of\:the\:cuboid=24\:cm}}$

➜ Height = 2x = 2 × 8 = 16 cm

➜ Hence height of the cuboid is 16 cm.

    $\boxed{\bold{Height\:of\:the\:cuboid=16\:cm}}$