Question

The length,breadth,and height of a cuboid are in the ratio 6:5:4 and its whole surface area is 33300cm .its volume is

Answer 1

As L:B:H = 6:5:4

let L = 6x
B = 5x
H = 4x

total surface area = 2(LB + BH + HL)

33300 = 2 (6x*5x + 5x*4x + 4x*6x)

33300 = 2(74x^2)

33300 = 148x^2

x^2 = 225

x = √225

x = 15cm

now
L = 6x = 6*15 = 90cm
B = 5x = 5*15 = 75cm
H = 4x = 4 * 15 = 60cm

Volume = L*B*H

Volume = 90*75*60

Volume = 405000 cm^3

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Answer 2

Given:

The length, breadth and height of a cuboid are in the ratio 6:5:4 and its whole surface area is 33300cm.

To find:

The volume of cuboid.

Solution:

The volume of cuboid is 405000 centimetre cube.

To answer this question, we should follow the following steps:

As given,

The length, breadth and height of a cuboid are in the ratio 6:5:4.

Let the common ratio between length, breadth and height of cuboid be x.

So,

The length of a cuboid = 6x

The breadth of a cuboid = 5x

The height of a cuboid = 4x

The whole surface area of a cuboid = 33300cm

Also,

The whole surface area of a cuboid

$= 2(lb \: + bh \: + hl)$

where l = length, b = breadth and h = height of the cuboid.

So,

$33300 = 2(6x \times 5x + 5x \times 4x + 4x \times 6x)$

$33300 = 2( {30x}^{2} + {20x}^{2} + {24x}^{2} )$

$33300 = 2( {74x}^{2} )$

${x}^{2} = \frac{33300}{2 \times 74}$

$= 225$

On taking square root on both sides, we get

$x = 15$

(neglecting x = -15, as length cannot be negative)

So,

The length of a cuboid = 6x = 6(15) = 90 cm

The breadth of a cuboid = 5x = 5(15) = 75 cm

The height of a cuboid = 4x = 4(15) = 60 cm

So,

Volume of cuboid

$= l \times b \times h$

$= 90 \times 75 \times 60$

$= 405000 \: {cm}^{3}$

Hence, the volume of the cuboid is 405000 centimetre cube.