Advertisements
Advertisements
Question
Water is flowing at the rate of 2.52 km/h through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.
Solution
Increase in the level of water in half an hour, h = 3.15 m = 315 cm
Radius of the water tank, r = 40 cm
Volume of water that falls in the tank in half an hour = πr2h
= π×402×315
= 5,04,000π cm3
Rate of flow of water = 2.52 km/h
Length of water column in half an hour =`2.52/2` = 1.26 km = 1,26,000 cm
Let the internal diameter of the cylindrical pipe be d.
Volume of the water that flows through the pipe in half an hour = `pi xx(d/2)^2xx126000cm^2`
We know
Volume of the water that flows through the pipe in half an hour = Volume of water that falls in the tank in half an hour
`=>pixx(d/2)^2xx126000= 504000pi`
`=>(d/2)^2=4`
`=>d^2=16`
`=>d= 4 "cm"`
Thus, the internal diameter of the pipe is 4 cm.
APPEARS IN
RELATED QUESTIONS
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]`
A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. Determine the internal diameter of the shell.
The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.
The surface areas of two spheres are in the ratio of 4 : 25. Find the ratio of their volumes.
The total surface area of a hemisphere of radius 7 cm is
From a solid cylinder whose height is 15 cm and diameter 16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Use π = 3.14)
In Figure 3, a decorative block is shown which is made of two solids, a cube, and a hemisphere. The base of the block is a cube with an edge 6 cm and the hemisphere fixed on the top has a diameter of 4⋅2 cm. Find
(a) the total surface area of the block.
(b) the volume of the block formed. `("Take" pi = 22/7)`
A metal cuboid of measures 16 cm × 11 cm × 10 cm was melted to make coins. How many coins were made, if the thickness and diameter of each coin was 2 mm and 2 cm respectively? (π = 3.14)
The internal and external radii of a spherical shell are 3cm and 5cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder. Also find the total surface area of the cylinder. (Take `pi = 22/7`)
Find the surface area of a sphere of radius 7 cm.
Solution :
The surface area of the sphere = 4πr2
= `4 xx 22/7 xx square^2`
= `4 xx 22/7 xx square`
= `square xx 7`
∴ The surface area of the sphere = `square` sq.cm.
