Advertisements
Advertisements
Question
Two circular cylinders of equal volume have their heights in the ratio 1 : 2 Ratio of their radii is
Options
- \[1 : \sqrt{2}\]
- \[\sqrt{2}: 1\]
1 : 2
1 : 4
Solution
Let V1 and V2 be the volume of the two cylinders with h1 and h2 as their heights:
Let r1 and r2 be their base radius.
It is given that
`V_1 = V_2 " and " h_1/h_2 = 1/2`
`pir_1^2 h_1 = pir_22 h_2`
`⇒ (r_1^2)/(r_2^2) = h_2/h_1`
`⇒(r_1^2)/(r_2^2) = 2`
`⇒(r_1)/(r_2) =sqrt(2)/1`
APPEARS IN
RELATED QUESTIONS
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find
(i) Its inner curved surface area,
(ii) The cost of plastering this curved surface at the rate of Rs 40 per m2.
`["Assume "pi=22/7]`
Find the curved surface area and total surface area of a cylinder, the diameter of whose base is 7 cm and height is 60 cm.
A well is dug 20 m deep and it has a diameter of 7 m. The earth which is so dug out is spread out on a rectangular plot 22 m long and 14 m broad. What is the height of the platform so formed?
A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 5 cm. It is drawnout into a wire of diameter 1 mm. What will be the length of the wire so formed?
From a tap 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 one hour.
The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm2.
A cylindrical tube, open at both ends, is made of metal. The 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.
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.
The dimensions of a car petrol tank are 50 cm × 32 cm × 24 cm, which is full of petrol. If a car's average consumption is 15 km per liter, find the maximum distance that can be covered by the car.
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.
