If the height of the cylinder is halved and the diameter is doubled, by what factor will the volume of the cylinder change?
A) 2
B) 4
C) 6
D) 8
Submit
Hint
Formulas
Geometry
(MGSE8.G.9) Know Formulas For Volume
ID: 135003
Answers
Answered by
5
hello friend , here is your answer
____________________
previous volume = πr²h
if diameter is doubled , i.e.
d=2r×2=4r
so , radius changed =2r
height =h/2
present volume = π×2r×2r×h/2
=2πr²h
=2× previous volume
thus volume is increased by factor 2
____________________
____________________
previous volume = πr²h
if diameter is doubled , i.e.
d=2r×2=4r
so , radius changed =2r
height =h/2
present volume = π×2r×2r×h/2
=2πr²h
=2× previous volume
thus volume is increased by factor 2
____________________
Answered by
1
Case 1:-
Height of the cylinder(h1) =h
Diameter of the cylinder (d1)=d
Radius of the cylinder (r1)=r=d/2
Volume of the cylinder (V1)= π(r1)²h1
=πr²h
Case 2:-
Height of the cylinder (h2)=h/2
Diameter of the cylinder (d2)= 2d
Radius of the cylinder (r2)= 2d/2=d=2r
Volume of the cylinder(V2)=π(2r)²(h/2)
=2πr²h =2V1
Therefore, the volume of the cylinder will change by the factor of 2.
Similar questions
Physics,
8 months ago
Social Sciences,
8 months ago
Social Sciences,
8 months ago
Science,
1 year ago
Math,
1 year ago
History,
1 year ago
Math,
1 year ago