Advertisements
Advertisements
Question
The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Prove that its height and radius are equal.
Solution
We have,
Let radius of cylinder be 'r'.
Let height of cylinder be 'h'.
`("Curved surface area of cylinder")/("total surface area of cylinder") = 1/2`
`(2pirh)/(2pir(h + r)) = 1/2`
`h/((h + r)) = 1/2`
2h = h + r
2h - h = r
h = r
Height = Radius
Hence proved.
APPEARS IN
RELATED QUESTIONS
Find the curved surface area and total surface area of a cylinder, the diameter of whose base is 7 cm and height is 60 cm.
The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find its curved surface area and total surface area.
In the middle of a rectangular field measuring 30m × 20m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.
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?
Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of copper weighs 8.4 gm.
If the height of a cylinder is doubled and radius remains the same, then volume will be ______.
In a cylinder, if radius is halved and height is doubled, the volume will be ______.
Find the lateral surface area, total surface area and the volume of the following cylinders: Diameter = 10m, High = 7m
Curved surface area of a cylinder of radius h and height r is ______.
How many solid right circular cylinders of radius 2 cm and height 3 cm can be made by melting a solid right circular cylinder of diameter 12 cm and height 15 cm?
