If the total surface area of the cubical room is 27 cm2. Find the leng

1.	If the total surface area of the cubical room is 27 cm2. Find the length of the longest rod inside the cubical room.1. 1/√6 cm2. 2√2/√3 cm3. 3√2/√3 cm4. 3√3/√2 cm
Answer» Correct Answer - Option 4 : 3√3/√2 cm Given: TSA = 27 cm² Formula used: TSA = 6a² (where a is the side of the cube) Diagonal = length of the longest rod inside the cubical room = a√3 Calculations: According to the question, 6 × a² = 27 ⇒ a² = 27/6 ⇒ a2 = 9/2 ⇒ a = 3/√2 cm ⇒ Diagonal = (3/√2) × √3 ⇒ Diagonal = 3√3/√2 cm ∴ The length of the longest rod inside the cubical room is 3√3/√2 cm.

If the total surface area of the cubical room is 27 cm2. Find the length of the longest rod inside the cubical room.1. 1/√6 cm2. 2√2/√3 cm3. 3√2/√3 cm4. 3√3/√2 cm

Answer» Correct Answer - Option 4 : 3√3/√2 cm

Given:

TSA = 27 cm²

Formula used:

TSA = 6a² (where a is the side of the cube)

Diagonal = length of the longest rod inside the cubical room = a√3

Calculations:

According to the question, 6 × a² = 27

⇒ a² = 27/6

⇒ a2 = 9/2

⇒ a = 3/√2 cm

⇒ Diagonal = (3/√2) × √3

⇒ Diagonal = 3√3/√2 cm

∴ The length of the longest rod inside the cubical room is 3√3/√2 cm.

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