Advertisements
Advertisements
प्रश्न
An open cylindrical vessel of internal diameter 7 cm and height 8 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is `3 1/2` cm and height 8 cm. Find the volume of water required to fill the vessel. If this cone is replaced by another cone, whose height is `1 3/4` cm and the radius of whose base is 2 cm, find the drop in the water level.
उत्तर
Diameter of the base of the cylinder = 7 cm
Therefore, radius of the cylinder = `7/2` cm
Volume of the cylinder = πr2h
= `22/7 xx 7/2 xx 7/2 xx 8`
= 308 cm3
Diameter of the base of the cone = `7/2 cm`
Therefore, radius of the cone = `7/4 cm`
Volume of the cone = `1/3pir^2h`
= `1/3 xx 22/7 xx 7/4 xx 7/4 xx 8`
= `77/3 cm^3`
On placing the cone into the cylindrical vessel, the volume of the remaining portion where the water is to be filled
= `308 - 77/3`
= `(924 - 77)/3`
= `847/3`
= 282.33 cm3
Height of new cone = `1 3/4 = 7/4 cm`
Radius = 2 cm
Therefore, volume of new cone
= `1/3pir^2h`
= `1/3 xx 22/7 xx 2 xx 2 xx 7/4`
= `22/3 cm^3`
Volume of water which comes down = `77/3 - 22/3 cm^3 = 55/3 cm^3` ...(1)
Let h be the height of water which is dropped down.
Radius = `7/2 cm`
∴ Volume = `pir^2h = 22/7 xx 7/2 xx 7/2 xx h` ...(2)
From (1) and (2)
`77/2 h = 55/3`
`=> h = 55/3 xx 2/77`
`=> h = 10/21`
Drop in water level = `10/21` cm
APPEARS IN
संबंधित प्रश्न
If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find (i) radius of its base (ii) its volume. [Use π = 3.14]
From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed. Find the volume of the remaining solid.
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.
The total surface area of a solid cylinder is 616 cm2. If the ratio between its curved surface area and total surface area is 1 : 2; find the volume of the cylinder.
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 diameter of the cross-section of a water pipe is 5 cm. Water flows through it at 10km/hr into a cistern in the form of a cylinder. If the radius of the base of the cistern is 2.5 m, find the height to which the water will rise in the cistern in 24 minutes.
If the circumference of a conical wooden piece is 484 cm then find its volume when its height is 105 cm.
Collect some old postcards. You can also use thick paper of size 14 cm x 9 cm.
Fold the postcard along the width to make pipe 1. Join the ends with cello tape.
Take another postcard and fold it along the length to make pipe 2. Join the ends with tape.
- Guess which pipe can take more sand inside it. Hold it on a plate and pour sand to check your guess. Was your guess correct? Discuss.
A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?
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.
