Advertisements
Advertisements
प्रश्न
Oil is stored in a spherical vessel occupying `3/4` of its full capacity. Radius of this spherical vessel is 28 cm. This oil is then poured into a cylindrical vessel with a radius of 21 cm. Find the height of the oil in the cylindrical vessel (correct to the nearest cm). Take π = `22/7`
उत्तर
Radius of spherical vessel, R = 28 cm
Radius of cylindrical vessel, r = 21 cm
Let, the height of cylindrical vessel be h cm
Volume of oil in sphere = `3/4 xx 4/3 πR^3`
= `22/7 xx 28 xx 28 xx 28`
Then, volume of oil in cylindrical vessel = Volume of oil in spherical vessel
`\implies π xx r^2h = 22/7 xx 28 xx 28 xx 28`
`\implies 22/7 xx 21 xx 21 xx h = 22/7 xx 28 xx 28 xx 28`
`\implies h = (28 xx 28 xx 28)/(21 xx 21)`
= `(4 xx 4 xx 28)/(3 xx 3)`
= 49.78 cm
APPEARS IN
संबंधित प्रश्न
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
`["Assume "pi=22/7]`
Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?
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.
The inner radius of a pipe is 2.1 cm. How much water can 12 m of this pipe hold?
Find the volume of the cylinder if the circumference of the cylinder is 132 cm and height is 25 cm.
Two solid cylinders, one with diameter 60 cm and height 30 cm and the other with radius 30 cm and height 60 cm, are metled and recasted into a third solid cylinder of height 10 cm. Find the diameter of the cylinder formed.
The radius and height of a cylinder are in the ratio of 5 : 7 and its volume is 550 cm. Find its radius. (Take π = 22/7)
A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder. (Take `22/7` for π)
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 school provides milk to the students daily in a cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto an height of 12 cm, find how many litres of milk is needed to serve 1600 students.
