Ratio of the volumes of a right circular cylinder and a sphere is 1:3.
Ratio of the radii of the cylinder and sphere is 1:3. If the sum of the
height and radius of the base of the cylinder is 78 cm, then what will
be the height of the cylinder?
Please give a correct answer. Unnecessary things will not be cooperated. Right answers will be marked 'Brainliest'
Answers
the answer will be 72 cm.
Step-by-step explanation:
Given:-
Ratio of the volumes of a right circular cylinder and a sphere is 1:3. Ratio of the radii of the cylinder and sphere is 1:3. If the sum of the height and radius of the base of the cylinder is 78 cm.
To find:-
what will be the height of the cylinder?
Solution:-
Given that
Ratio of the radii of the cylinder and sphere is 1:3.
Let the radius of the cylinder be X cm
r=X cm
Let the radius of the sphere = 3X cm
R=3X cm
Ratio of the volumes of a right circular cylinder and a sphere is 1:3.
We know that
Volume of a cylinder = πr^2h cubic units
Volume of a Sphere= (4/3)πR^3 cubic units
=>πr^2h : (4/3)πR^3 = 1:3
=>πr^2h / (4/3)πR^3 = 1/3
=>r^2h / (4/3)R^3 = 1/3
=>X^2 h / (4/3)(3X)^3 = 1/3
=>X^2 h / (4/3)(27X^3) = 1/3
Cancelling X^2 term
=>h / (4/3)27X = 1/3
=>h/4(9X) = 1/3
=>h/36X = 1/3
On applying cross multiplication then
=>3h = 36X
=>h = 36X/3
=>h = 12X cm-----------(1)
Now,
Given that
the sum of the height and radius of the base of the cylinder is 78 cm.
h+r = 78 cm
=>h+ X = 78 cm
On Substituting the value of h from (1) then
=> 12X+X = 78
=>13 X = 78
=>X = 78/13
=>X = 6 cm
Radius of the Cylinder =6 cm
On Substituting the value of the radius in (1) then
h = 12×6
h = 72 cm
Height of the Cylinder = 72 cm
Answer:-
The value of the height of the cylinder is 72 cm
Used formulae:-
- Volume of a cylinder = πr^2h cubic units
- Volume of a Sphere= (4/3)πR^3 cubic units