Question

the area of three faces of a cuboid are in the ratio 2:3:4 and its volume is 9000 cm3 . the length of the shortest edge is

Answer 1

hope the answer in attachment helps you!!

Answer 2

Answer:

The length of the shortest edge is 15 cm.

Step-by-step explanation:

Given : The area of three faces of a cuboid are in the ratio 2:3:4 and its volume is 9000 cm³.

To find : The length of the shortest edge?

Solution :

Let the edges of cuboid be a,b,c.

The area of three faces of a cuboid are in the ratio 2:3:4.

i.e. $a b:bc :ca=2:3:4$

Let the ratio be k,

So, ab=2k , bc=3k, ca=4k

Multiply all these,

$ab\times bc\times ca=2k\times 3k\times 4k$

$a^2b^2c^2=24k^3$

$(abc)^2=24k^3$ ....(1)

The volume of the cuboid is $V=abc$

i.e. $abc=9000$

Substitute in (1),

$(9000)^2=24k^3$

$81000000=24k^3$

$k^3=\frac{81000000}{24}$

$k^3=3375000$

$k=\sqrt[3]{3375000}$

$k=150$

So, $ab=2k=2(150)=300$

$bc=3k=3(150)=450$

$ca=4k=4(150)=600$

We know, $abc=9000$ ....(2)

Divide (2) by bc,

$\frac{abc}{bc}=\frac{9000}{bc}$

$a=\frac{9000}{450}=20$

Divide (2) by ac,

$\frac{abc}{ac}=\frac{9000}{ac}$

$b=\frac{9000}{600}=15$

Divide (2) by ab,

$\frac{abc}{ab}=\frac{9000}{ab}$

$c=\frac{9000}{300}=30$

The dimensions of the cuboid is $15\times 20\times 30$ cm.

Therefore, The length of the shortest edge is 15 cm.