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The sum of the length, breadth and height of a cuboid is 6√3  cm and the length of its diagonal is 2√3 cm. The total surface area of the cuboid is

(a) 48 cm 2   (b) 72 cm 2   (c) 96 cm 2   (d) 108 cm 2

 

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Transcript

Question 13 The sum of the length, breadth and height of a cuboid is 6√3 cm and the length of its diagonal is 2√3 cm. The total surface area of the cuboid is (a) 48 cm2 (b) 72 cm2 (c) 96 cm2 (d) 108 cm2 Let Length = l Breadth = b Height = h Given that Sum of the length, breadth and height of a cuboid is 6√3 cm l + b + h = 6√𝟑 cm Also, given that Length of its diagonal is 2√3 cm. √(𝒍^𝟐+𝒃^𝟐+𝒉^𝟐 )=𝟐√𝟑 We need to find Total surface area of the cuboid Now, Total Surface area of cuboid = 2(lb + bh + lh) From (1) l + b + h = 6√𝟑 cm Squaring both sides (𝒍+𝒃+𝒉)^𝟐=(𝟔√𝟑)^𝟐 𝑙^2+𝑏^2+ℎ^2+2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=6^2 × (√3)^2 𝑙^2+𝑏^2+ℎ^2+2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=36 × 3 𝒍^𝟐+𝒃^𝟐+𝒉^𝟐+2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=108 𝟏𝟐+2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=108 2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=108−12 2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=96 𝑙^2+𝑏^2+ℎ^2+2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=6^2 × (√3)^2 𝑙^2+𝑏^2+ℎ^2+2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=36 × 3 𝒍^𝟐+𝒃^𝟐+𝒉^𝟐+2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=108 𝟏𝟐+2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=108 2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=108−12 2𝑙𝑏+2𝑏ℎ+2𝑙ℎ=96 Total Surface Area = 96 cm2 So, the correct answer is (c)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.