Advertisements
Advertisements
प्रश्न
A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.
उत्तर
Case 1:
Height = h cm = 30 cm
Diameter = d cm = 18 cm
Radius = r cm = 9 cm
∴ Volume = (πr2h) or (π(9 )2(30 )) = 2430π cm3
Case 2:
Height = h cm = 18 cm
Diameter = d cm = 30 cm,
Radius = r cm = 15 cm
∴ Volume = (πr2h) or (π(15 )2(18 )) = 4050π cm3
Hence, the ratio of the volumes of the two cylinders formed is 3:5.
APPEARS IN
संबंधित प्रश्न
Find the height of the cylinder whose volume is 1.54 m3 and diameter of the base is 140 cm?
A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 metre per second. In how much time the tank will be filled?
If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, find:
(i) radius of its base
(ii) volume of the cylinder
[Use ` pi` = 3.14]
The difference between inside and outside surfaces of a cylindrical tube 14 cm long is 88 sq. cm. If the volume of the tube is 176 cubic cm, find the inner and outer radii of the tube.
If the height of a cylinder is doubled and radius remains the same, then volume will be
The inner diameter of a well is 4.20 metre and its depth is 10 metre. Find the inner surface area of the well. Find the cost of plastering it from inside at the rate Rs.52 per sq.m.
Find the area of base and radius of a cylinder if its curved surface area is 660 sqcm and height is 21 cm.
A rectangular strip 36cm x 22cm is rotated about the longer side. Find the volume and the total surface area of the cylinder formed.
A cylindrical tube, open at both ends, is made of metal. The bore (internal diameter) of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal. Also, find the weight of the tube if 1 cm3 of the metal weighs 1.42 g.
Two cylinders with equal volume will always have equal surface areas.
