Advertisements
Advertisements
Question
A solid is in the shape of a hemisphere of radius 7 cm, surmounted by a cone of height 4 cm. The solid is immersed completely in a cylindrical container filled with water to a certain height. If the radius of the cylinder is 14 cm, find the rise in the water level.
Solution
Volume of solid = `1/3πr^2h + 2/3πr^3`
= `1/3πr^2 (h + 2r)`
= `π/3 xx (7)^2 xx (4 + 2 xx 7)`
= `π/3 xx 49 xx 18`
= 294π cm3
Let y be the height rise of water in a cylindrical cylinder with radius R = 14 cm.
∴ Volume of water rise in a cylindrical container = Volume of solid immersed
πR2y = 294π
`\implies` π(14)2y = 294π
∴ y = `294/(14 xx 14)`
= `21/14`
= `3/2`
= 1.5 cm
Hence, The rise in the water level is y = 1.5 cm
APPEARS IN
RELATED QUESTIONS
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 well of diameter 2m is dug14m deep. The earth taken out of it is spread evenly all around it to form an embankment of height 40cm. Find width of the embankment?
A reservoir in the form of the frustum of a right circular cone contains 44 × 107 litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir. (Take: π = 22/7)
A copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform thickness and length 10 m. Find the thickness of the wire.
150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.
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.
A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of water
- displaced out of the cylinder
- left in the cylinder.
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 cube of side 6 cm is cut into a number of cubes, each of side 2 cm. The number of cubes formed is
A hemispherical bowl of internal diameter 30 cm is full of a liquid. This liquid is poured into cylindrical bottles of diameter 5 cm and height 6 cm each. How many bottles are required?
