Advertisements
Advertisements
Question
A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by
Options
4.5 cm
3
4 cm
2 cm
Solution
Radius of the sphere = 6 cm.
Volume of the sphere
`=4/3pir^3`
`=4/3 pi xx 6 xx 6 xx 6`
and
Radius of the cylinder = 8 cm
Volume of the cylinder
`=pir^2h`
`=pi xx 8 xx 8 xx h`
Therefore,
Volume of the sphere = volume of the cylinder
`4/3pi(6)^3 = pi(8)^2 h`
or
`h = (4 xx 72)/64 = 4.5 cm`
APPEARS IN
RELATED QUESTIONS
In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km2, show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.
The largest sphere is carved out of a cube of side 10.5 cm. Find the volume of the sphere.
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 height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be \[\frac{1}{27}\] of the volume of the given cone, then the height above the base at which the section has been made, is
A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and the slant height of the conical portion is 53 m, find the area of canvas needed to make the tent.
66 cubic cm of silver is drawn into a wire 1 mm in diameter. Calculate the length of the wire in metres.
Choose the correct answer of the following question:
A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone is
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. The height of the pillar is
The height of a conical tent is 14 m and its floor area is 346.5 m2. How much canvas, 1.1 wide, will be required for it?
Match the column:
| (1) surface area of cuboid | (A) πr2h |
| (2) surface area of closed right cylinder | (B) 2πr(h + r) |
| (3) Total surface area of right cone | (C) πrl + πr2 |
| (4) Total surface area of hemisphere | (D) 3πr3 |
| (E) 3πr2 | |
| (F) 2[lb + bh + lh] |
