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)
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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