If the radius of a cylinder is decreased by 50 percent and the height increased by 50 percent then find percentage decreased in volume?
Share
If the radius of a cylinder is decreased by 50 percent and the height increased by 50 percent then find percentage decreased in volume?
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Answer:
62.5%
Step-by-step explanation:
Let r be the radius and h be the height of the cylinder.
∴ Original volume,V = πr²h
(i) Radius is increased by 50%:
New radius, r₁ = r - 50% of r
= r - (50/100) * r
= r - r/2
= r/2.
(ii) Height increased by 50%:
New height, h₁ = h + 50% of h
= h + (50/100) * h
= h + h/2
= 3h/2
∴ New volume,V₁ = πr₁²h₁
= π(r/2)²(3h/2)
= (3/8)πr²h
Decrease in volume = V - V₁
= (1 - 3/8)πr²h
= (5/8)πr²h
%Decrease in volume = [5/8πr²h/πr²h] * 100%
= [5/8] * 100%
= 62.5%.
Therefore, decrease in volume = 62.5%.
Hope it helps!
Verified answer
The radius of a cylinder is decreased by 50 percent and the height increased by 50 percent.
so the
volume before reducing and increasing was
decrease in radius
=> r-50/100 r
=> r-1/2r
=> r-r/2
=> 2r-r/2
=> r/2
Now
increase in height
=> h+50/100h
=>h+1/2h
=> h+h/2
=> 2h+h/2
=> 3h/2
Now
new volume=
volume percent= orginal volume - new volume/original volume*100
=>
=>