Advertisements
Advertisements
Question
Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. What is the ratio of their radii ?
Solution
Let r1 and r2 be the radii of two right circular cylinders and h1 and h2 be the heights.
Since,
Both the cylinder has the same volume.
Therefore,
`pir_1^2 h_1 = pir_2^2 h_2`
`(r_1/r_2)^2 = h^2/h_1`
`(h_1 :h_2 = 1:2 , "given")`
`(r_1/r_2)^2 = (2/1)`
`r_1 :r_2 = sqrt2 : 1`
APPEARS IN
RELATED QUESTIONS
A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied in a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel.
A sphere of maximum volume is cut-out from a solid hemisphere of radius r, what is the ratio of the volume of the hemisphere to that of the cut-out sphere?
A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?
A cylindrical vessel 32 cm high and 18 cm as the radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, the radius of its base is
A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, then find its width.
The radius of the base of a cone is 5 cm and its height is 12 cm. Its curved surface area is
The area of the base of a right circular cone is 154 cm2 and its height is 14 cm. Its curved surface area is
The slant height of the frustum of a cone is 4 cm and the perimeters (i.e. circumferences) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
The volume of a sphere is 4851 cm3. Its diameter is ______.
A cylindrical tank has a radius of 154 cm. It is filled with water to a height of 3 m. If water to a height of 4.5 m is poured into it, what will be the increase in the volume of water in kl?
