Question

If a nd b are the roots of the equation f(x)=0, then the equation f '(x) = 0 will have at least one root between a and b, provided

(a) f(x) is continuous in [a,b]
(b) f'(x) exists in [a, b]
(c) both (a) and (b)
(d) f(a) = f(b)​

Answer 1

Volume of cylinder=πr

2

h

Let the radius of cylinder A be r and cylinder B be R

∴r=2R(Given)

Let the height of Cylinder A b h and B be H

∴2h=H(Given)

Volume of Cylinder A will be =πr

2

h

Volume of Cylinder B will be =πR

2

H

Substituting r=2R and H=2h in the formulas we get

Volume of Cylinder A will be =π(2R)

2

h=π4R

2

h

Volume of Cylinder B will be =πR

2

(2h)

Ratio=

Volume of B

Volume of A

=

πR

2

2h

π4R

2

h

(Canselling the like terms)

=2