Question

find the total surface area and lateral surface area of a cube whose volume is 729cm cube and the ans is 486 cm cube but what is the solution​

Answer 1

vol. = 729

a^3 = 729

a = 9

Total surface area = 6a^2

= 6 (9)^2

= 486cm^2

Lateral surface area= 4a^2

= 4 (9)^2

= 324..cm^2

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Answer 2

Answer:

The TSA of the cube is 486 cm² and LSA is 324 cm².

Step-by-step explanation:

Given :

Volume of the cube = 729 cm³

To find :

Total Surface Area and Lateral Surface Area of the cube

Solution :

First find the measure of the Cube's side.

Let the Side be y

★ $\textsf{\underline{\underline{Measure of the Side :}}}$

$\sf{Volume\:of\:Cube=\purple{{S}^{3}}}$

$\sf{\implies} \: 729 = {y}^{3} \\ \\ \sf{\implies} \:y = \sqrt[3]{729} \\ \\\sf{\implies} \: y = 9$

Side of the Cube = 9 cm

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Total Surface Area : }}}$

$\sf{Formula =\purple{6( {Side}^{2})}}$

$\sf{\implies} \:6 \times {9}^{2} \\ \\ \sf{\implies} \:6 \times 81 \\ \\ \sf{\implies} \:486 \: {cm}^{2}$

Total Surface Area = 486 cm²

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Lateral Surface Area : }}}$

$\sf{Formula = \purple{4 {(Side)}^{2}}}$

$\sf{\implies} \:4 \times {9}^{2} \\ \\ \sf{\implies} \:4 \times 81 \\ \\ \sf{\implies} \:324 \: {cm}^{2}$

Lateral Surface Area = 324 cm²

$\therefore$ The TSA of the cube is 486 cm² and LSA is 324 cm².