Question

If the difference between the total surface area and lateral surface area is 392cm^2, find its total surface area

Answer 1

Correct Question:

If the difference between the total surface area of cube and lateral surface area of cube is 392 cm², Find its total surface area.

Answer:

• Total surface area of cube = 1176 cm²

Step-by-step explanation:

Given:

• TSA of cube - CSA of cube = 392 cm²

To Find:

• Total Surface area of cube.

We know that,

⇒ Total Surface area of cube = 6a²

And,

⇒ Curved surface area of cube = 4a²

Now,

⇒ TSA - CSA = 392 cm²

⇒ 6a² - 4a² = 392

⇒ 2a² = 392

⇒ a² = 392/2

⇒ a² = 196

⇒ a = √196

⇒ a = 14 cm

Now, we will calculate TSA of cube,

⇒ Total Surface area of cube = 6a²

⇒ Total Surface area of cube = 6 × 14²

⇒ Total Surface area of cube = 6 × 196

⇒ Total Surface area of cube = 1176 cm²

Hence, Total surface area of cube = 1176 cm²

Answer 2

$\huge{\underline{\underline{\color{darkblue}{\bf{Given}}}}}$

$\sf Difference\;between\;Total\;surface\;area$

$\sf and\;lateral\;surface\;area\;of\;cube\;is\;392cm^2$

$\large\bold\blue{NOTE}$

$\sf Total\;surface\;area\;of\;cube\;=\;6a^2$

$\sf Lateral\;surface\;area\;of\;cube\;=\;4a^2$

$\huge{\underline{\underline{\color{darkblue}{\bf{Solution}}}}}$

$\sf 6a^2-4a^2\;=\;392$

$\sf 2a^2\;=\;392$

$\sf a^2\;=\frac{392}{2}$

$\sf a^2\;=\;196$

$\sf a\;=\sqrt{196}\;=\;14cm$

$\sf Total\;surface\;area\;of\;cube$

$\sf 6a^2$

$\sf =\;6\;×\;(14)^2$

$\sf =\;6\;×\;196$

$\sf =\;1176cm^2$

$\small{\boxed{\bf{\red{Total\: surface\: area\: of\: cube\: =\: 1176cm^2}}}}$