CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard

Practice Questions CBSE - Maths Class 10 (2023 Boards) →
Class 10
Solutions of Sample Papers for Class 10 Boards

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

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

 

Slide26.JPG

Slide27.JPG
Slide28.JPG
Slide29.JPG

 

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)

Go Ad-free
Davneet Singh's photo - Co-founder, Teachoo

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