Question

Eind the TSA anodLSA of the
cube whose
side is 21 cm​

Answer 1

AnswEr:

⋆ CUBE:

$\setlength{\unitlength}{0.65cm}\begin{picture}(2,3)\thicklines\put(2,6){\line(1,0){3.3}}\put(2,9){\line(1,0){3.3}}\put(5.3,9){\line(0,-1){3}}\put(2,6){\line(0,1){3}}\put(0,7.3){\line(1,0){3.3}}\put(0,10.3){\line(1,0){3.3}}\put(0,10.3){\line(0,-1){3}}\put(3.3,7.3){\line(0,1){3}}\put(2,6){\line(-3,2){2}}\put(2,9){\line(-3,2){2}}\put(5.3,9){\line(-3,2){2}}\put(5.3,6){\line(-3,2){2}}\put(3.4,5.5){\sf21 cm}\put(0,6.3){\sf21 cm}\put(5.5,7.5){\sf21 cm}\end{picture}$

$\;\;\bullet\;\;\sf Side\;of\;the\;cube\;(a)\;is\; \bf{21\;cm}$

$\rule{150}{2}$

$\bf \underline{\bigstar\;\;Let's\;head\;to\;the\; Question\;now\;:}\\\\ \sf As\;we\;know\;that,$

$\maltese\;{\underline{\sf{Total\;surface\;area\;of\;cube\;:\;6a^2}}}\\\\ :\implies\sf 6 \times 21 \times 21\\\\ :\implies{\underline{\boxed{\sf{\pink{2646\;cm^2}}}}}\;\bigstar$

$\maltese\;{\underline{\sf{Total\;surface\;area\;of\;cube\;:\;4a^2}}}\\\\ :\implies\sf 4 \times 21 \times 21\\\\ :\implies{\underline{\boxed{\sf{\pink{1764\;cm^2}}}}}\;\bigstar\\\\ \therefore\;\sf \underline{Hence,\;TSA\;and\;LSA\;of\;cube\;are\;2646\;cm^2\;and\;1764\;cm^2\; respectively.}$

$\rule{150}{2}$

$\star\;{\underline{\underline{\sf{\purple{Additional\; Information}}}}}$

• Cube is a solid three-dimensional figure, having 6 square faces, 8 vertices and 12 edges.

• It is also known as regular hexahedron.

• All the sides of cube are equal.

★ Formulas related to cube:

• Volume of cube : (edge)³ = a³

• TSA of cube : 6a³

• LSA of cube : 4a²

• Diagonal of face of the cube : $\sf \sqrt{2} \times a$

• Diagonal of cube : $\sf \sqrt{3} \times a$

• Edge of cube : $\sf (volume)^{1/3}$

Answer 2

Given ,

• Side of cube (a) = 21 cm

We know that , the total surface area of cube is given by

$\boxed{ \sf{TSA = 6 {(a)}^{2} }}$

Thus ,

TSA = 6 × (21)²

TSA = 6 × 441

TSA = 2646 cm²

∴The TSA of cube is 2646 cm²

Now , the lateral surface area of cube is given by

$\boxed{ \sf{LSA = 4 {(a)}^{2} }}$

Thus ,

LSA = 4 × (21)²

LSA = 4 × 441

LSA = 1764 cm²

∴The LSA of cube is 1764 cm²