Advertisements
Advertisements
Question
Radius of a cylinder is r and the height is h. Find the change in the volume if the height is doubled and the radius is halved.
Solution
∵ Volume of a cylinder = πr2h
Where, h is height and r is radius of base of the cylinder.
If height is doubled and the radius is halved,
i.e. h = 2h and `r = r/2`
∴ Volume = `pi xx (r/2) xx (r/2) xx 2h`
= `pi xx r^2/4 xx 2h`
= `(pir^2h)/2`
Hence, volume became half of the original volume.
APPEARS IN
RELATED QUESTIONS
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;
- the internal volume of the container in m3.
A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the:
(i) radius of the cylinder
(ii) curved surface area of the cylinder
Take π = 3.1
A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm3 of the metal weights 7.7 g.
Two right circular solid cylinders have radii in the ratio 3 : 5 and heights in the ratio 2 : 3. Find the ratio between their volumes.
The radius of two right circular cylinder are in the ratio of 2 : 3 and their heights are in the ratio of 5: 4 calculate the ratio of their curved surface areas and also the ratio of their volumes.
The total surface area of a cone whose radius is `r/2` and slant height 2l is ______.
The dimensions of a godown are 40 m, 25 m and 10 m. If it is filled with cuboidal boxes each of dimensions 2 m × 1.25 m × 1 m, then the number of boxes will be ______.
Two cylinders A and B are formed by folding a rectangular sheet of dimensions 20 cm × 10 cm along its length and also along its breadth respectively. Then volume of A is ______ of volume of B.
Two cylinders of same volume have their radii in the ratio 1 : 6, then ratio of their heights is ______.
From a pipe of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the pipe in 1 hour.
