Advertisements
Advertisements
Question
Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ______.
Solution
Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is 3 : 1.
Explanation:
Let r1, r2 be the radii and h1, h2 be the heights of two cylinders.
Given, `h_1/h_2 = 1/9`
Now, according to the question,
`pir_1^2h_1 = pir_2^2h_2` ...[∵ Volume of cylinder = πr2h]
⇒ `r_1^2/r_2^2 = h_2/h_1`
⇒ `(r_1/r_2)^2 = 9/1`
⇒ `r_1/r_2 = sqrt(9)/1`
⇒ `r_1/r_2 = 3/1`
Hence, r1 : r2 = 3 : 1
APPEARS IN
RELATED QUESTIONS
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
`["Assume "pi=22/7]`
A cylindrical can, whose base is horizontal and of radius 3.5 cm, contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can, calculate:
- the total surface area of the can in contact with water when the sphere is in it;
- the depth of water in the can before the sphere was put into the can.
A cylinder of circumference 8 cm and length 21 cm rolls without sliding for `4 1/2` seconds at the rate of 9 complete rounds per second. Find the area covered by the cylinder in `4 1/2` seconds.
A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate: the total area of the internal surface, excluding the base.
If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is
In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If its height is 20 cm, the volume of the material in it is
A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimeters of iron has been used in making the tube?
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 volume of a cylinder whose radius r is equal to its height is ______.
Radius of a cylinder is r and the height is h. Find the change in the volume if the height is doubled.
