Question

two cubes each of volume 729cm sq m are joined end to end find the surface area of the resulting cuboid​

Answer 1

Answer:

answer for the given problem is 810 square cm

Answer 2

GivEn:

• Volume of two cubes : 729 cm³

To find:-

• surface area of the resulting cuboid.

SoluTion:

✇ Lets side of both cubes be a.

$\setlength{\unitlength}{0.65cm}\begin{picture}(2,3)\thicklines\put(2,6){\line(1,0){3.3}}\put(2,9){\line(1,0){3.3}}\put(5.3,9){\line(0,-1){3}}\put(2,6){\line(0,1){3}}\put(0,7.3){\line(1,0){3.3}}\put(0,10.3){\line(1,0){3.3}}\put(0,10.3){\line(0,-1){3}}\put(3.3,7.3){\line(0,1){3}}\put(2,6){\line(-3,2){2}}\put(2,9){\line(-3,2){2}}\put(5.3,9){\line(-3,2){2}}\put(5.3,6){\line(-3,2){2}}\put(3.4,5.5){\sf a}\put(0,6.3){\sf a}\put(5.5,7.5){\sf a}\end{picture}$

$\rule{150}2$

${\underline{\bf{\bigstar\;Now,\; According\;to\;QuesTion\;:}}}$

Two cubes each of volume 729cm³ are joined end to end to form a cuboid.

So, As we know that,

$\maltese\;{\boxed{\sf{\pink{Volume\;of\;cube\;:\;a^3}}}}\\\\ \sf Therefore,\\\\ \dashrightarrow\sf a^3 = 729\\\\ \;\;\dag\;\sf \underline{Taking\;cube\;root\;both\;sides\;:}\\\\ \dashrightarrow\sf \sqrt[3]{a^3} = \sqrt[3]{729}\\\\ \dashrightarrow{\underline{\boxed{\sf{\purple{a = 9\;cm}}}}}$

If two sides of cube joined end to end to form cuboid. Therefore, length of resulting cuboid is twice the side of cube. And the breadth and height remain same as the side of cube.

$\therefore$ Side of cuboid = 2a.

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\put(8,5.5){2a}\put(4,6.3){a}\put(11.2,7.5){a}\end{picture}$

$\rule{150}2$

$\dashrightarrow\sf Side_{cuboid} = 2 \times 9\\\\ \dashrightarrow{\underline{\boxed{\sf{\purple{Side_{cuboid} = 18\;cm}}}}}$

${\underline{\bf{\bigstar\; Therefore,\;the\;TSA\;of\;cuboid\;is,}}}\\\\ \maltese\;{\boxed{\sf{\pink{Volume\;of\;cuboid\;:\;2(lb + bh + bl)}}}}\\\\ \dashrightarrow\sf 2(18 \times 9 + 9 \times 9 + 9 \times 18)\\\\ \dashrightarrow\sf 2(81 + 162 + 162)\\\\ \dashrightarrow\sf 2 \times 405\\\\ \dashrightarrow{\underline{\boxed{\sf{\green{810\;cm^2}}}}}\;\bigstar\\\\ \therefore\;\sf \underline{Hence,\;Total\;Surface\;Area\;of\;Cuboid\;is\; \bf{810\;cm^2}}$