help@askiitians.com

+91-87964 74404

Grade 12Differential Calculus

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

taniska

12 Years agoGrade 12

1 Answer

Arun Kumar

12 Years ago

Hi

$\\h_{cone}=r+rsin\theta \\r_{cone}=rcos\theta \\=>v=1(r+rsin\theta)(rcos\theta)^2/3 \\=>lnv=2ln(rcos\theta)+ln(r+rsin\theta)+lnc \\=>0=2(-sin\theta)/cos\theta+cos\theta/(1+sin\theta)=0 \\=>2sin\theta(1+sin\theta)=cos^2\theta \\=>1-sin^2\theta=2sin\theta+2sin^2\theta \\=>3sin^2\theta+2sin\theta-1=0 \\=>sin\theta={-2 \pm 4 \over 6}=1/3 \\=>h=r4/3=d*2/3$

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to move once over to level a playground. find the area of the playground in square m?

differential calculus

1 Answer Available

Last Activity: 3 Years ago

Find dy/DX when y=x^sinx+sin-1√x.

Please give me the solution of this problem.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

If domain of f(x) is [-1, 2], then find the domain of f([x]-x^2+4), where [ ]denotes greatest integer function.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

Example 20. (i) In a AABC, find the maxima and minima of u = sin A sin B sin C
where A + B + C = T
(ii) In a plane triangle ABC, find the maximum value of cosA cosB cosC.

differential calculus

1 Answer Available

Last Activity: 4 Years ago

View all Questions