|

 Krishnan Ramachandran's messages in the community 1 2 3 4 5 6 7 8 GO Go to Page...
Message
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
Q. Prove that det(adj A) = (det(A))n-1 where A is a invertible square matrix.
 Discussion Forums -> This Post 22 points    (4    in 5 votes )   [?]
1.The surface area increases approximately by 2k%
2.The volume increases approximately by 3k% for small k

Soln: Height of the new cone = H+K*H/100 where H is the height of the original cone
The semivertical angle 'A' is related as
cos A = H/L where L is the slant height
Also for the new cone ,
cos A = (H+kH/100)/L' where L' is the slant height of new cone

From above eqs.
L' = L+kL/100
We know
sin A = R/L
For the new cone,
sin A = R'/(L+kL/100)
From above eqs.
R' = R+kR/100

Total Surface Area = 2RH+R2
Total Surface area of new cone = 2(R+kR/100)(H+kH/100) + (R+kR/100)2

Increase in area = ((Area of new cone)/Area of original cone)-1
On solving ,
Increase = 2k/100
Therefore , percentage increase = 2k%

Volume = 1/3R2H
Volume of new cone = 1/3R'2H'    where R'=R+kR/100 , H'=H+kH/100
On solving
Percentage Increase =3k%

 1 2 3 4 5 6 7 8 GO Go to Page...
 Go to:  Select a forum   Board Exams - CBSE, ICSE, State Boards   Course Material   Computer Science   Physics   General Physics   Mechanics   Optics   Thermal Physics   Electricity   Magnetism   Modern Physics   Mathematics   Algebra   Trignometry   Analytical Geometry   Differential Calculus   Integral Calculus   Vectors   Chemistry   Physical Chemistry   Organic Chemistry   Inorganic Chemistry   Institutes & Courses   Coaching Institutes & Course Material   About IITs and JEE   Non IIT Institutes   Counselling Zone   Parents Corner   Parent Discussion Board   Biology (for Medical Entrance)   Botany   Zoology   Fun Zone   Lounge   Games, Puzzles and Quizzes   General Knowledge

Name

Mobile

E-mail

City

Class