Question

Find the volume of a rectangular box whose adjacent edges are 3x²y,4y²z and 5z²x respectively

Answer 1

Answer: Volume $60 {x}^{3} {y}^{3} {z}^{3} \: {unit}^{3}$

Solution:

To find the volume of a rectangular box whose adjacent edges are 3x²y,4y²z and 5z²x respectively

I.e

$length = 3 {x}^{2} y \\ \\ breadth = 4 {y}^{2} z \\ \\ height = 5 {z}^{2} x$
Volume of rectangular box

$= l \: \times b \times h \\ \\ = (3 {x}^{2} y) \times (4 {y}^{2} z) \times (5 {z}^{2} x) \\ \\ = 60 {x}^{3} {y}^{3} {z}^{3} \: {unit}^{3}$
Hope it helps you.

Answer 2

given, adjacent edges of rectangular box are 3x²y , 4y²z and 5z²x

let length of rectangle box , L = 3x²y

breadth of rectangular box , B = 4y²z

height of rectangular box, H = 5z²x

we know, volume of cuboid = Length × breadth × height

so, volume of rectangular box = L × B × H

= (3x²y) × (4y²z) × (5z²x)

= 60x³y³z³ = 60(xyz)³

hence, volume of rectangular box = 60(xyz)³