Advertisements
Advertisements
Question
A hemispherical tank full of water is emptied by a pipe at the rate of \[\frac{25}{7}\] litres per second. How much time will it take to half-empty the tank, If the tank is 3 metres in diameter?
Solution
Volume of half of hemispherical tank
`=2/3pir^3`
`=2/3 xx 22/7 xx (3/2)^3`
` = (49500)/7`ltr.
Amount of water emptied by pipe in 1 sec.`= 25/7`ltr
So, time taken
`=7/25 xx (49500)/7`
` = 1980 sec`
`= (1980)/60 min`
`= 33 min`
To half empty the tank line
` = 33/2`
` = 16.5 min`
APPEARS IN
RELATED QUESTIONS
A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of canvas required for the tent.
A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy. `[\text{Use}pi 22/7]`
An iron pole consisting of a cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that 1 cm3 of iron has 8 gram mass approximately. (Use : π = 355/115)
Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water . Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm .
A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 98 cm and the diameter of each of its hemispherical ends is 28 cm, find the cost of polishing the surface of the solid at the rate of 15 paise per sq cm.
A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, then find the total area of the canvas required.
The surface areas of a sphere and a cube are equal. Find the ratio of their volumes.
A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm3 . the radii of the top and bottom of the circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of the metal sheet used in making it.
A cylindrical tank has a radius of 154 cm. It is filled with water to a height of 3 m. If water to a height of 4.5 m is poured into it, what will be the increase in the volume of water in kl?
If the length of the diagonal of a cube is `5sqrt(3)` cm, find the total surface area.
Length of the diagonal of the cube = `square`
So, `square` = `5sqrt(3)`
⇒ Side = `square`
Total surface area of cube = `square`
= `square` × `square` × `square`
= `square` cm2
Hence, the total surface area is `square`.
