Question

the surface area of the six faces of a rectangular solid are 16 16 32 32 72 and 72 square cm to the volume of this​

Answer 1

Answer:

Volume  = 192 cm³

Step-by-step explanation:

Let say Sides of Rectangular solid are L , B & H

LB = 16

LH = 32

BH = 72

=> LH/LB = 32/16

=> H/B = 2

=> H = 2B

B (2B) = 72

=> B² = 36

=> B = 6

BH = 72

=> 6H = 72

=> H = 12

LB =16

=> L = 16/6 = 8/3

Volume = LBH = (8/3) * 6 * 12 = 192 cm³

or simply = LB * BH * LH = 16 * 32 * 72

=> (LBH)² = 16 * 16 * 2 * 2 * 36

Square rooting both side

=> LBH = 16 * 2 * 6

=> Volume  = 192 cm³

Answer 2

Answer:

Volume of the rectangular solid is 192 cm cube

Step-by-step explanation:

Formula used:

Volume of the cuboid = l*b*h cubic units

Let l, b and h be length, breadth and height of the rectangular solid respectively.

with loss of generality, we take

lb= 16 square cm.

bh= 32 square cm.

hl= 72 square cm.

Multiplying these we get

(lb)(bh)(hl)=(16)(32)(72)

$(lbh)^2=16*16*2*2*36$

$lbh=\sqrt{16*16*2*2*36}$

$lbh=16*2*6$

$lbh=192\:cm^3$