Advertisements
Advertisements
Question
The radius of the base of a right circular cylinder is doubled and the height is halved. What is the ratio of volume of the new cylinder to that of the original cylinder?
Solution
Let the radius of base of the original cylinder = r
And the height of the cylinder = h
Volume of original cylinder = π r2 h
Given that, the radius of new cylinder = 2r
And height= `"h"/(2)`
∴ Volume of new cylinder
= `π xx (2"r")^2 xx "h"/(2)`
= 2 x r2h
Ratio of volume of new cylinder to that of original cylinder
= `(2pi"r"^2"h")/(pi"r"^2"h")`
= 2 : 1.
APPEARS IN
RELATED QUESTIONS
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet are required for the same?
`["Assume "pi=22/7]`
The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?
`["Assume "pi=22/7]`
Rukhsar painted the outside of the cabinet, of measure 1 m × 2 m × 1.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet?
A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the
external diameter of the cylinder be 1.4 m and its length be 8 m, find the cost of painting it
on the outside at the rate of Rs. 10 per `m^2`.
Write the number of surfaces of a right circular cylinder.
Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is
Radius of base of a cylinder is 20 cm and its height is 13 cm, find its curved surface area and total surface area. (π = 3.14)
A well with 6 m diameter is dug. The earth taken out of it is spread uniformly all around it to a width of 2 m to form an embankment of height 2.25 m. Find the depth of the well.
If the height of a cylinder becomes `1/4` of the original height and the radius is doubled, then which of the following will be true?
The ratio of the radius and height of a cylinder is 2:3. If its volume is 12,936 cm3, find the total surface area of the cylinder.
