A rectangular sheet of paper 30 cm × 18 cm can be transformed into curved surface of a right circular cylinder in two ways either by rolling along its length or along its breadth. Find the ratio of the volumes of the two cylinders thus formed
Answers
Case1: when the sheet is folded along its length :
In this case, it forms a cylinder having height h1=18 cm and the circumference of its base equal to 30 cm.
Let the radius of its base be r1. Then,
2pi r1=30
r1=15/pi.
V1=pi r^2 h=pi*(15/pi)^2 cm3=4050/pi.cm3
Case.2
When the sheet folded along its breadth :
Heights h2=30cm and the circumference of its base equal to 18cm.
Let the radius be r2. Then,
2pi r2=18=(9/pi)
V2=pi r^2 h=(pi*(9/11)^2) cm^3 =2430/pi cm^3.
V1/v2=(4050/pi*pi/2430)=4050/2430=5/3
Ans.5:3.
Answer:
[5 : 3]
Step-by-step explanation:
Case1: when the sheet is folded along its length :
In this case, it forms a cylinder having height h1=18 cm and the circumference of its base equal to 30 cm.
Let the radius of its base be r1. Then,
2pi r1=30
r1=15/pi.
V1=pi r^2 h=pi*(15/pi)^2 cm3=4050/pi.cm3
Case.2
When the sheet folded along its breadth :
Heights h2=30cm and the circumference of its base equal to 18cm.
Let the radius be r2. Then,
2pi r2=18=(9/pi)
V2=pi r^2 h=(pi*(9/11)^2) cm^3 =2430/pi cm^3.
V1/v2=(4050/pi*pi/2430)=4050/2430=5/3
Ans.5:3.