Question
The area of a cylinder is 956m3. If the circular top is halved, what is the new volume?
Answers
Reiny
Your question is rather vague.
When you say that the circular top is halved, are you taking half of the diameter or half of the area ?
When you say that the circular top is halved, are you taking half of the diameter or half of the area ?
Anonymous
The radius is halved
Reiny
(same as diameter halved, anyway ....)
original:
radius r, height h
surface area = 2πrh + 2πr^2
= 956
πrh + πr^2 = 478
h = (478-πr^2)/(πr)
for new cylinder, height = h, radius = r/2
volume = π(r^2/4)(478-πr^2)/(πr)
= (478r - πr^3)/4
so the relationship depends on the value of r
Are you sure the area was 956 and not the volume?
then the volume would simply be 1/4 of the original, or 239 m^3
original:
radius r, height h
surface area = 2πrh + 2πr^2
= 956
πrh + πr^2 = 478
h = (478-πr^2)/(πr)
for new cylinder, height = h, radius = r/2
volume = π(r^2/4)(478-πr^2)/(πr)
= (478r - πr^3)/4
so the relationship depends on the value of r
Are you sure the area was 956 and not the volume?
then the volume would simply be 1/4 of the original, or 239 m^3