Question

If the difference between the total surface area and the lateral surface area of a cuboidal object ise 392 cmsquare. Find its total surface area

Answer 1

Answer:

Step-by-step explanation:

Answer 2

• The total surface area of the given cubical object is equal to 1176 cm² .

Given :- The difference between the total surface area and the lateral surface area of a cubical object is 392cm² .

To Find :- Total surface area of the cubical object ?

Formula used :-

• Total surface area (TSA) of cube = 6a²
• Lateral surface area (LSA) of cube = 4a²
• where a is the length of each side of the cube .

Solution :-

Let us assume that, the length of each side of given cubical object is equal to a cm .

So,

→ Total surface area of cubical object = 6a²

and,

→ Lateral surface area of cubical object = 4a²

A/q,

→ Total surface area of cubical object - Lateral surface area of cubical object = 392 cm²

→ 6a² - 4a² = 392

→ 2a² = 392

dividing both sides by 2,

→ a² = 196

→ a² = (±14)²

square root both sides,

→ a = ± 14 cm

since length of sides of a cubical object can't be in negative . Therefore, we can conclude that, the length of each side of given cubical object is equal to 14 cm .

therefore,

→ Total surface area of cubical object = 6a²

putting a = 14 cm we get,

→ Total surface area of cubical object = 6•(14)²

→ Total surface area of cubical object = 6 × 196

→ Total surface area of cubical object = 1176 cm² (Ans.)

Hence, required total surface area is equal to 1176 cm² .

Shortcut :-

→ 6a² - 4a² = 392

→ 2a² = 392

dividing both sides by 2,

→ a² = 196

therefore,

→ TSA = 6a² = 6 × 196 = 1176 cm² .

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