Question 13 - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

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
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(b) 72 cm
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(c) 96 cm
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(d) 108 cm
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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)

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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