Question

The surface area of the three coterminous faces of a cuboid are 6 cm 2 , 15 cm 2 , and 10 cm2 respectively. What is the volume of the cuboid?

Answer 1

lb=6
bh=15
lh=10
lb×bh×lh=6×15×10
l^2×b^2×h^2=900
lbh=30

Answer 2

The volume of the cuboid is 30 cm³.

Step-by-step explanation:

Given : The surface area of the three coterminous faces of a cuboid are 6 cm² ,15 cm² , and 10 cm² respectively.

To find : What is the volume of the cuboid?

Solution :

Let l,b,h be the dimensions of the cuboid.

The surface area of the three coterminous faces of a cuboid are 6 cm² , 15 cm² , and 10 cm² respectively.

i.e. $l\times b=6$ ...(1)

$b\times h=15$ ...(2)

$h\times l=10$ ...(3)

Volume of the cuboid is $V=lbh$

Multiply (1),(2) and (3),

$l\times b\times b\times h\times h\times l=6\times 15\times 10$

$l^2\times b^2\times h^2=900$

$(lbh)^2=900$

$lbh=\sqrt{900}$

$lbh=30$

Therefore, the volume of the cuboid is 30 cm³.

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