Question

Three solid metal cubes with edges 15dm, 2m, 25dm are melted and formed into a new solid cube.
Find the surface area of the new cube?​(formula)

Answer 1

$\textbf{Given:}$

$\textsf{Three solid metal cubes with edges 15dm, 2m,}$

$\textsf{25dm are melted and formed into a new solid cube}$

$\textbf{To find:}$

$\textsf{Surface area of the new cube}$

$\textbf{Solution:}$

$\textsf{Let 'a' be the length of the new cube formed}$

$\textsf{As per given data,}$

$\textsf{Volume of 3 cubes = Volume of the new cube}$

$\mathsf{15^3+20^3+25^3=a^3}$

$\mathsf{5^3(3^3+4^3+5^3)=a^3}$

$\mathsf{5^3(27+64+125)=a^3}$

$\mathsf{5^3(216)=a^3}$

$\mathsf{5^3{\times}6^3=a^3}$

$\mathsf{(5{\times}6)^3=a^3}$

$\mathsf{30^3=a^3}$

$\impliesboxed{\mathsf{a=30\;dm}}$

$\mathsf{Now,}$

$\textsf{Surface area of the new cube}$

$\mathsf{=6a^2}$

$\mathsf{=6(30)^2}$

$\mathsf{=6(900)}$

$\mathsf{=5400\;dm^2}$

$\textbf{Answer:}$

$\mathsf{Surface\;area\;of\;the\;cube\;is\;5400\;dm^2}$

Answer 2

Answer:

5400 dm^2

Step-by-step explanation:

Let ’a’ be the length of the new cube formed

\textsf{As per given data,}As per given data,

\textsf{Volume of 3 cubes = Volume of the new cube}Volume of 3 cubes = Volume of the new cube

\mathsf{15^3+20^3+25^3=a^3}153+203+253=a3

\mathsf{5^3(3^3+4^3+5^3)=a^3}53(33+43+53)=a3

\mathsf{5^3(27+64+125)=a^3}53(27+64+125)=a3

\mathsf{5^3(216)=a^3}53(216)=a3

\mathsf{5^3{\times}6^3=a^3}53×63=a3

\mathsf{(5{\times}6)^3=a^3}(5×6)3=a3

\mathsf{30^3=a^3}303=a3

\impliesboxed{\mathsf{a=30\;dm}}\impliesboxeda=30dm

\mathsf{Now,}Now,

\textsf{Surface area of the new cube}Surface area of the new cube

\mathsf{=6a^2}=6a2

\mathsf{=6(30)^2}=6(30)2

\mathsf{=6(900)}=6(900)

\mathsf{=5400\;dm^2}=5400dm2