The ratio of the radii of two spheres is 1:2. The two spheres are melted together to form a cylinder of height which is 12 times its radius. So what is the ratio of the radius of the smaller sphere and the cylinder?
Answers
Answer:
Step-by-step explanation:
Let radius of given sphers are r and R and height of cylinders after reshaping are h and H
Given : r:R=1:2 and
height of cylinder after reshaping is H and radius =x
H=12x
We know after reshaping only volume will remain same as material is same quantity
so Sum of volume of spheres = volume of cylinder
and we get required ratio as 1:1
further solution is in the attached pic
Answer: 1:1
Step-by-step explanation: Let the radius of small sphere be r1
then the radius of bigger sphere be r2
and it is given in the question that r2=2r1
now both the spheres are melted and converted into a cylinder
so 1 thing of our interest is that the combined volume of these two spheres will be equal to the volume of cylinder
also let the radius of cylinder be rh
so equating the two volumes we get
πrh2h = 4/3πr13 +4/3πr23
⇒rh2*12 rh = 4/3 r13 + 4/3 (2r1)3
⇒12 rh3 = 12 r13
so the ratio of radius of smaller sphere and cylinder will be (1:1)