Question

. Find the length of edge of a cube with following
volume:
(i) 343 cm3 (ii) 729 cm
(iii) 1728 cm
(iv) 8000 cm​

Answer 1

$\large{\mathcal{\underline{\underline{\red{QUESTION:}}}}}$

Find the length of edge of a cube with following  volume:

• 343 cm³
• 729 cm³
• 1728 cm³
• 8000 cm³

$\large{\mathcal{\underline{\underline{\red{SOLUTION:}}}}}$

$\sf 1).Volume\;of\;cube=343\;cm^{3}\\ \\ {\underline{\bf We\;know\;that,}}\\ \\ \longrightarrow \sf Volume\;of\;cube=a^{3}\\ \\ {\underline{\bf Now,\;put\;the\;values,}}\\ \\ \longrightarrow \sf 343 =a^{3}\\ \\ \longrightarrow {\boxed{\sf a=7\;cm}}\\ \\ \rule{200}{2}$

$\sf 2).Volume\;of\;cube=729\;cm^{3}\\ \\ {\underline{\bf We\;know\;that,}}\\ \\ \longrightarrow \sf Volume\;of\;cube=a^{3}\\ \\ {\underline{\bf Now,\;put\;the\;values,}}\\ \\ \longrightarrow \sf 729 =a^{3}\\ \\ \longrightarrow {\boxed{\sf a=9\;cm}}\\ \\ \rule{200}{2}$

$\sf 3).Volume\;of\;cube=1728\;cm^{3}\\ \\ {\underline{\bf We\;know\;that,}}\\ \\ \longrightarrow \sf Volume\;of\;cube=a^{3}\\ \\ {\underline{\bf Now,\;put\;the\;values,}}\\ \\ \longrightarrow \sf 1728 =a^{3}\\ \\ \longrightarrow {\boxed{\sf a=12\;cm}}\\ \\ \rule{200}{2}$

$\sf 4).Volume\;of\;cube=8000\;cm^{3}\\ \\ {\underline{\bf We\;know\;that,}}\\ \\ \longrightarrow \sf Volume\;of\;cube=a^{3}\\ \\ {\underline{\bf Now,\;put\;the\;values,}}\\ \\ \longrightarrow \sf 8000 =a^{3}\\ \\ \longrightarrow {\boxed{\sf a=20\;cm}}$

Answer 2

Question :

Find the length of edge of a cube with following volume:

$(i) 343 \: cm^3 \\ (ii)729 \: cm^3 \\(iii)1728 \: cm^3 \\ (iv)8000 \: cm^3$

Solution :

$\boxed{\purple{Edge\:of\:cube=\sqrt[3]{Volume}}}$

$\rule {193}{1}$

$(i) 343 \: cm^3$

$\implies Edge\:of\:the \: cube=\sqrt[3]{Volume} \\ \implies Edge\:of\:the \: cube=\sqrt[3]{343} \: cm \\ \implies Edge\:of\:the \: cube=\sqrt[3]{7 \times 7 \times 7} \: cm \\ \implies Edge\:of\:the \: cube = 7 \: cm$

$\boxed{\green{\therefore{The \:length \:of \:the\: edge\:of\:the\:cube \:is\:7\:cm.}}}$

$\rule {193}{1}$

$(ii) 729\: cm^3$

$\implies Edge\:of\:the \: cube=\sqrt[3]{Volume} \\ \implies Edge\:of\:the \: cube=\sqrt[3]{729} \: cm \\ \implies Edge\:of\:the \: cube=\sqrt[3]{9 \times 9 \times 9} \: cm \\ \implies Edge\:of\:the \: cube = 9 \: cm$

$\boxed{\green{\therefore{The \:length \:of \:the\: edge\:of\:the\:cube \:is\:9\:cm.}}}$

$\rule {193}{1}$

$(iii) 1728\: cm^3$

$\implies Edge\:of\:the \: cube=\sqrt[3]{Volume} \\ \implies Edge\:of\:the \: cube=\sqrt[3]{1728} \: cm \\ \implies Edge\:of\:the \: cube=\sqrt[3]{12\times 12 \times 12} \: cm \\ \implies Edge\:of\:the \: cube = 12 \: cm$

$\boxed{\green{\therefore{The \:length \:of \:the\: edge\:of\:the\:cube \:is\:12\:cm.}}}$

$\rule {193}{1}$

$(iv)8000 \: cm^3$

$\implies Edge\:of\:the \: cube=\sqrt[3]{Volume} \\ \implies Edge\:of\:the \: cube=\sqrt[3]{8000} \: cm \\ \implies Edge\:of\:the \: cube=\sqrt[3]{20 \times 20\times 20} \: cm \\ \implies Edge\:of\:the \: cube = 20 \: cm$

$\boxed{\green{\therefore{The \:length \:of \:the\: edge\:of\:the\:cube \:is\:20\:cm.}}}$

$\rule {193}{1}$