The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the original one.
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The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the original one.
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GIVEN :-
TO FIND :-
TO KNOW :-
★ Volume of Cylinder = πr²h
Here ,
HOW TO SOLVE ?
We will find volume in both the given cases by the formula. In case 1 , Radius is r and Height is h. In case 2 , Radius is r/2 and Height is 2h. Then we will divide and can easily find out the ratio.
SOLUTION :-
♦ Let us assume a Cylinder with Radius 'r' and Height 'h'.
↦ Original Volume = πr²h ------(1)
Now ,
♦ Radius is halved and Height is doubled.
↦ New Volume = π(r/2)²(2h)
↦ New Volume = π(r²/4)(2h)
↦ New Volume = πr²h/2 -------(2)
✠ We have to find ratio of New Volume to Original Volume.
So,
New Volume / Original Volume
ㅤㅤㅤㅤㅤㅤㅤ= [πr²h/2] / [πr²h]
ㅤㅤㅤㅤㅤㅤㅤ= 1/2
Hence , when radius is halved and height is doubled , the ratio of New Volume to Original Volume is 1:2.
MORE FORMULA :-
★ Volume of Cone = (1/3)πr²h
★ Volume of Cube = edge³
★Volume of Cuboid = l × b × h
★Volume of Sphere = (4/3)πr³
★Volume of Hemisphere = (2/3)πr³
Step-by-step explanation:
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