Question

How many cubes of each side 0.5cm are required to build a cubes of volume 27 cm cube

Answer 1

$\huge\mathbb{\underline{SOLUTION:-}}$

$\bold{given:-}\begin{cases}\sf{edge\:of\:cube_1=0.5cm}\\ \sf{Volume\:of\:new\:cube_2=27cm{}^{3}}\end{cases}$

• We have to find how many cubes of side 0.5 cm will be required to form the cube whose volume is 27cubic .cm

$\bf\underline{\underline{According\:To\: Question:-}}$

• FIND THE VOLUME OF CUBE WHOSE EDGE IS 0.5CM

$\boxed{\sf{Volume\:of\:cube=side{}^{3}}}$

• Side=0.5cm

$\sf\implies Volume =0.5\times 0.5\times 0.5\\ \\ \sf\implies Volume=0.25\times 0.5\\ \\ \sf\implies Volume=0.125cm{}^{3}$

$\boxed{\sf{Volume\:of\:cube_1=0.125cm{}^{3}}}$

• Now we have to find how many cube will be required to form $\sf 27cm{}^{3}$

$\boxed{\sf {No.\:of\:cubes=\frac{Volume\:of\:cube_2}{Volume\:of\:cube_1}}}$

$\sf\implies cubes\: required=\frac{27}{0.625}\times \frac{1000}{1000}\\ \\ \sf\implies multipy\:with\:1000 \:to\: remove\:the\:point\\ \\ \sf\implies No.\:of\:cubes=\cancel{\frac{27000}{625}}\\ \\ \sf\implies Number\:of\:cubes=43.2$

$\boxed{\sf{\purple{cubes\: required=43.2}}}$

$\bf\underline{\underline{\red{Some\:Extra\: knowledge:-}}}$

$\sf 1) Volume\:of\:cube=side{}^{3}\\ \\ \sf 2) volume\:of\: cuboid= l\times b\times h\\ \\ \sf 3) Surface\:Area\:of\:Cube=6a{}^{2}\\ \\ \sf 4) surface\:area\:of\: cuboid=2(lb+bh+bh)\\ \\ \sf 5) Diagonal\:of\:cube=a\sqrt{3}\\ \\ \sf 6) Diagonal\:of\: cuboid=\sqrt{l{}^{2}+b{}^{2}+h{}^{2}}$

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