Question

Find the length of the cube formed when the following are arranged : one cube of side 2 cm, one cube of side 3 cm , three cuboids of dimensions 2cm ×2cm ×3cm and three cuboids of dimensions 2cm×3cm×3cm

Answer 1

Answer:

The length of side of the cube formed is 5 cm

Step-by-step explanation:

Formula used:

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

Volume of a cube = a³ cubic units

Let x be the length of the side the cube formed

As per given data,

Volume of the cube formed

=(Volume of cube of side 2 cm) + (Volume of cube of side 3 cm) + 3*(Volume of cuboid of dimensions 2cm*2cm*3cm)+3*(Volume of cuboid of dimensions 2cm*3cm*3cm)

$=2^3+3^3+3*(2*2*3)+3*(2*3*3)$

$=8+27+3*(12)+3*(18)$

$=8+27+36+54$

$=125\:cm^3$

Volume of the cube formed$=125\:cm^3$

$\implies\:x^3=125$

$\implies\:x=\sqrt[3]{125}$

$\implies\:x=5\:cm$