At lunch Claire is drinking her juice out of an aluminum can She claims that if the radius of the can is doubled, the volume of the can will be greater than if the height of the can is doubled

True

Step-by-step explanation:

Can is shaped in the form of a cylinder :

Volume, V of a cylinder = πr²h

Volume if radius is doubled and height remains the same :

r = 2r

V = π(2r)²h

V = 4πr²h

Volume if height is doubled and radius remains the same ;

V = πr²h

If h = 2h

V = 2πr²h

Radius doubled ; V = 4πr²h

Height doubled ; V = 2πr²h

Hence, volume of can is greater with Radius doubled than with height doubled.