Advertisements
Advertisements
Question
A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5 cm. Find its capacity.
Solution
Diameter of the hemisphere = 21 cm
Therefore, radius of the hemisphere = 10.5 cm
Volume of the hemisphere `=2/3pir^3= 2/3xx22/7xx 10.5xx 10.5xx10.5 = 2425.5 "cm"^3`
Height of the cylinder
= Total height of the vessel - Radius of the hemisphere = 14.5 - 10.5= 4 cm
Volume of the cylinder = `pir^2h = 22/7xx10.5xx10.5xx4=1386 "cm"^3`
Total Volume= Volume of hemispherical part + Volume of cylinder = 1386 + 2425.5 = 3811.5 cm3
APPEARS IN
RELATED QUESTIONS
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
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.
A solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of radius 3.5 cm and height 3 cm.Find the number of cones so formed.
The capacity of a certain cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its height and length are 10 m and 2.5 m respectively.
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)
Choose the correct answer of the following question:
The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is
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)`
Arrange the given objects according to their volume
A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square?
A rectangular examination hall having seats for 500 candidates has to be built so as to allow 4 cubic metres of air and 0.5 square metres of floor area per candidate. If the length of hall be 25 m, find the height and breadth of the hall.
