Question

Cubes A, B, C having edges 18 cm, 24 cm and 30 cm respectively are moulded into a new cube D. Find the edge of the bigger cube D.

Answer 1

Edge of cube A = 18 cm
$\therefore$ Volume = $a^3=(18{)}^{3}c{m}^3=5832c{m}^3$
Edge of cube B= 24 cm
$\therefore$ Volume = $(30{)}^3=27000c{m}^3$
Volume of A,B,C cubes
= 58332 + 13824 + 27000= 46656 $c{m}^3$
$\therefore$ Volume of cube D = 46656 $c{m}^3$
$\therefore$ Edge of cube D = $\sqrt[3]{346656}$
= $\sqrt[3]{336\times 36\times 36}=\sqrt[3]{3(36{)}^3}=36$ cm