Advertisements
Advertisements
Question
Find the volume of the largest cylinder formed when a rectangular piece of paper 44 cm by 33 cm is rolled along its :
- shorter side.
- longer side.
Solution
i. Length of a rectangular paper = 44 cm
Breadth of a rectangular paper = 33 cm
When the paper is rolled along its shorter side, i.e. breadth, we have
Height of cylinder = h = 44 cm
Circumference of cross-section = 2πr = 33 cm
`=> 2 xx 22/7 xx r = 33`
`=> r = (33 xx 7)/(2 xx 22) = 5.25 cm`
∴ Volume of cylinder = πr2h
= `22/7 xx 5.25 xx 5.25 xx 44`
= 3811.5 cm3
ii. Length of a rectangular paper = 44 cm
Breadth of a rectangular paper = 33 cm
When the paper is rolled along its longer side , i.e. length, we have
Height of cylinder = h = 33 cm
Circumference of cross-section = 2πr = 44 cm
`=> 2 xx 22/7 xx r = 44`
`=> r = (44 xx 7)/(2 xx 22) = 7 cm`
∴ Volume of cylinder = πr2h
= `22/7 xx 7 xx 7 xx 33`
= 5082 cm3
APPEARS IN
RELATED QUESTIONS
If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find (i) radius of its base (ii) its volume. [Use π = 3.14]
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
`["Assume "pi=22/7]`
A cylindrical water tank of diameter 2.8 m and height 4.2 m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4 m s–1. Calculate, in minutes, the time it takes to fill the tank.
3080 cm3 of water is required to fill a cylindrical vessel completely and 2310 cm3 of water is required to fill it upto 5 cm below the top. Find :
- radius of the vessel.
- height of the vessel.
- wetted surface area of the vessel when it is half-filled with water.
The difference between the outer curved surface area and the inner curved surface area of a hollow cylinder is 352 cm2. If its height is 28 cm and the volume of material in it is 704 cm3; find its external curved surface area.
A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.
A glass cylinder with a diameter 20 cm water to a height of 9 cm. A metal cube of 8 cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder. (Take π = 3.142)
The diameter of the cross-section of a water pipe is 5 cm. Water flows through it at 10km/hr into a cistern in the form of a cylinder. If the radius of the base of the cistern is 2.5 m, find the height to which the water will rise in the cistern in 24 minutes.
Volume of a cylinder with radius h and height r is ______.
A hollow garden roller of 42 cm diameter and length 152 cm is made of cast iron 2 cm thick. Find the volume of iron used in the roller.
