Last updated at April 15, 2021 by Teachoo

Transcript

Example 2 The volume of a cube is increasing at a rate of 9 cubic centimeters per second. How fast is the surface area increasing when the length of an edge is 10 centimeters ?Let ๐ be length of side V be Volume t be time per second We know that Volume of cube = (side)3 V = ๐๐ Also it is given that Volume of cube is increasing at rate of 9 cubic cm/sec. Therefore ๐ ๐ฝ/๐ ๐ = 9 Putting V = ๐๐ (ใ๐(๐ฅใ^3))/๐๐ก = 9 ใ๐๐ฅใ^3/๐๐ก . ๐๐ฅ/๐๐ฅ = 9 ใ๐๐ฅใ^3/๐๐ฅ . ๐๐ฅ/๐๐ก = 9 3๐๐ . ๐ ๐/๐ ๐ = 9 ๐๐ฅ/๐๐ก = 9/ใ3๐ฅใ^2 ๐ ๐/๐ ๐ = ๐/๐^๐ Now, We need to find fast is the surface area increasing when the length of an edge is 10 centimeters i.e. ๐ ๐บ/๐ ๐ for x = 10 We know that Surface area of cube = 6 ร Side2 S = 6๐ฅ2 Finding ๐ ๐บ/๐ ๐ ๐๐/๐๐ก = (๐(6๐ฅ^2))/๐๐ก = (๐(6๐ฅ2))/๐๐ก . ๐๐ฅ/๐๐ฅ = 6. (๐(๐ฅ2))/๐๐ฅ . ๐๐ฅ/๐๐ก = 6 . (2x) . ๐๐ฅ/๐๐ก = 12๐ฅ . ๐ ๐/๐ ๐ = 12๐ฅ . ๐/๐๐ = ๐๐/๐ (From (1): ๐ ๐/๐ ๐ = ๐/๐^๐ ) For ๐ฅ= 10 cm ๐๐/๐๐ก = 36/10 ๐๐/๐๐ก = 3.6 Since surface area is in cm2 & time is in seconds, ๐๐/๐๐ก = 3.6 ๐๐2/๐ ๐ ๐บ/๐ ๐ = 3.6 cm2 /s

Examples

Example 1
Deleted for CBSE Board 2021 Exams only

Example 2 Deleted for CBSE Board 2021 Exams only You are here

Example 3 Deleted for CBSE Board 2021 Exams only

Example 4 Important Deleted for CBSE Board 2021 Exams only

Example 5 Deleted for CBSE Board 2021 Exams only

Example 6 Deleted for CBSE Board 2021 Exams only

Example 7

Example 8 Important

Example 9 Important

Example 10

Example 11 Important

Example 12

Example 13 Important

Example 14

Example 15

Example 16

Example 17 Important

Example 18

Example 19

Example 20

Example 21 Deleted for CBSE Board 2021 Exams only

Example 22 Deleted for CBSE Board 2021 Exams only

Example 23 Deleted for CBSE Board 2021 Exams only

Example 24

Example 25

Example 26

Example 27

Example 28 Important

Example 29

Example 30 Important

Example 31

Example 32 Important

Example 33 Important

Example 34

Example 35 Important

Example 36

Example 37 Important

Example 38 Important

Example 39

Example 40 Important

Example 41 Important

Example 42 Important Deleted for CBSE Board 2021 Exams only

Example 43 Important Deleted for CBSE Board 2021 Exams only

Example 44 Important Deleted for CBSE Board 2021 Exams only

Example 45 Important

Example 46 Important

Example 47 Important

Example 48 Important

Example 49 Deleted for CBSE Board 2021 Exams only

Example 50 Important

Example 51

Chapter 6 Class 12 Application of Derivatives

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.