Question

If the areas of three adjacent faces of a cuboid are 16 cm², 12 cm² and 27 cm², find the volume of the cuboid.

Answer 1

Answer:

and is 5184

Step-by-step explanation:

area of cuboid is lbh

Answer 2

Step-by-step explanation:

We know that a cuboid has length,breadth and height

Now areas of three adjacent faces of a cuboid are 16 cm², 12 cm² and 27 cm²

lb= 16 cm² ...eq1

bh = 12 cm²....eq2

hl= 27 cm².... eq3

divide eq1 and 2

$\frac{lb}{bh} = \frac{16}{12} \\ \\ \frac{l}{h} = \frac{4}{3} \\ \\ l = \frac{4h}{3}$

put the value in eq3

$h\times\frac{4h}{3} = 27 \\ \\ {h}^{2} = \frac{27 \times 3}{4} \\ \\ {h}^{2} = \frac{81}{4} \\ \\ h = \frac{9}{2}$

$bh = 12 \\ \\ b = \frac{12\times2}{ 9 } \\ \\ b = \frac{8}{ 3}$

$hl = 27 \\ \\ l = \frac{27\times 2}{9 } \\ \\ l = 6$

Now,volume of cuboid

$V= l\:\times\:b\:\times\:h\\\\=\frac{9}{2}\times\frac{8}{ 3}\times6 \:{cm}^{3}\\\\=72{cm}^{3}$

Volume of cuboidal shape 72 c-cube

Hope it helps you