There are 3 sphere having r cm radius which are completely fit (vertical manner) in a cylinder. Those sphere cut out from the cylinder. What the ratio of total surface area of all three sphere to curved surface area of cylinder?
There are 3 sphere having r cm radius which are completely fit (vertical manner) in a cylinder. Those sphere cut out from the cylinder. What the ratio of total surface area of all three sphere to curved surface area of cylinder?
1). 1 ∶ 1
2). 2 ∶ 3
3). 3 ∶ 1
4). 4 ∶ 5
1 answers
Solution :
It is given that all the three spheres fit correctly into the cylinder so, the height of the cylinder will be equal to the sum of diameter of the three spheres,
===> $h = 3 d$ ( 'h' is the height of the cylinder and 'd' is the diameter of the sphere.)
We know that $d = 2r$ so,
$h = 3×2r = 6r$
$h = 6r$
Total Surface Area of a Sphere $= 4 \pi r^2$
Total Surface Area of 3 Spheres $= 3× 4 \pi r^2 = 12 \pi r^2$
Curved Surface Area of Cylinder $= 2 \pi r h$
Total Surface Area of $3$ Spheres : Curved Surface Area of Cylinder
$= 12 \pi r^2 ÷ 2 \pi r h$
$= 6 r ÷ h$
$= 6 r ÷ 6 r ( h = 6r )$
$= 1 : 1$
So, the correct option is 1).1 : 1
