Advertisements
Advertisements
प्रश्न
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the hemisphere is immersed in the tub. If the radius of the hemi-sphere is 3.5 cm and height of the cone outside the hemisphere is 5 cm, find the volume of the water left in the tub (Take π = 22/7)
उत्तर
To find the volume of the water left in the tube, we have to subtract the volume of the hemisphere and cone from volume of the cylinder.
For right circular cylinder, we have
r = 5cm
h = 9.8 cm
The volume of the cylinder is
V1 = πr2h
`=22/7xx5^2xx9.8`
= 770cm
For hemisphere and cone, we have
r = 3.5 cm
h = 5 cm
Therefore the total volume of the cone and hemisphere is
`V_2=1/3pir^2h+2/3pir^3`
`=1/3xx22/7xx3.5^2xx5+2/3xx22/7xx3.5^3`
= 154 cm3
The volume of the water left in the tube is
V = V1 - V2
Hence, the volume of the water left in the tube is V = 616cm3
APPEARS IN
संबंधित प्रश्न
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.
A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much is canvas cloth required to just cover the heap?
A path 2m wide surrounds a circular pond of diameter 40m. how many cubic meters of gravel are required to grave the path to a depth of 20cm ?
The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use it =`22/7`)
The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Find the ratio of their volumes.
A solid metallic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm. Find the number of spherical balls obtained.
Choose the correct answer of the following question:
A metallic solid sphere of radius 9 cm is melted to form a solid cylinder of radius 9 cm. The height of the cylinder is
A cubical ice-cream brick of edge 22 cm is to be distributed among some children by filling ice-cream cones of radius 2 cm and height 7 cm up to the brim. How many children will get the ice-cream cones?
The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is 1056 cm2 and the volume of material in it is 1056 cm3. Find its internal and external radii. Given that the height of the cylinder is 21 cm.
The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used up on writing 3300 words on an average. How many words can be written in a bottle of ink containing one fifth of a litre?
