Math, asked by pMahajan5474, 11 months ago

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

Answers

Answered by Anonymous
4

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

Answered by Anonymous
12

\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}}}}

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