Advertisements
Advertisements
प्रश्न
Water is flowing through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second. Determine the rise in level of water in the tank in half an hour.
Advertisements
उत्तर
We have,
the internal radius of the cylindrical pipe, r = 2/2 = 1 cm and
the base radius of cylindrical tank, R = 40 cm.
Also, the rate of flow, h = 0.4 m/s = 40 cm/s
Let the rise in level of water be H.
Now,
The volume of water flowing out of the cylindrical pipe in 1 sec =πr2h = π × 1 × 1 × 40 = 40π cm3
As,
Volume of water in the cylindrical tank = Volume of standing water in cylindrical pipe
⇒πR2H = 72000π
⇒R^2H = 72000`
⇒ 40 × 40 × H = 7200H
`rArr H = 72000/(40xx40)`
∴ H = 45 cm
So, the rise in level of water in the tank in half an hour is 45 cm.
Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.
APPEARS IN
संबंधित प्रश्न
504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area.
[Use π=22/7]
If the total surface area of a solid hemisphere is 462 cm2 , find its volume.[Take π=22/7]
The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
[Use `pi = 22/7`]
A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.
A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per
100 cm2
A cylindrical tub, whose diameter is 12 cm and height 15 cm is full of ice-cream. The whole ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice-cream cone ?
A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel. `[\text{Use}pi=22/7]`
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
A solid metal sphere of 6 cm diameter is melted and a circular sheet of thickness 1 cm is prepared. Determine the diameter of the sheet.
A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid.
Two solid cones A and B are placed in a cylindrical tube as shown in fig .16.76. The ratio of their capacities are 2: 1 . Find the heights and capacities of the cones . Also, find the volume of the remaining portion of the cylinder.
A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be poured into cylindrical bottles of diameter 5 cm and height 6 cm each. Find the number of bottles required.
Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single large cube. Find the edge of the new cube formed.
Match the following columns:
| Column I | Column II |
| (a) The radii of the circular ends of a bucket, in the form of the frustum of a cone of height 30 cm, are 20 cm and 10 cm respectively. The capacity of the bucket is ........cm3. |
(p) 2418π |
| (b) The radii of the circular ends of a conical bucket of height 15 cm are 20 and 12 cm respectively. The slant height of the bucket is ........ cm. |
(q) 22000 |
| (c) The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. The total surface area of the bucket is .........cm2. |
(r) 12 |
| (d) Three solid metallic spheres of radii 3 cm, 4 cm and 5 cm are melted to form a single solid sphere. The diameter of the resulting sphere is ........ cm. |
(s) 17 |
If the volumes of a cube is 1728 cm³, the length of its edge is equal to ______.
If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr2.
3 cubes each of 8 cm edge are joined end to end. Find the total surface area of the cuboid.
