Advertisements
Advertisements
प्रश्न
A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.
Advertisements
उत्तर
Radius of cylinder = 3 cm
Height of cylinder = 6 cm
Radius of hemisphere = 2 cm
Height of cone = 4 cm
Volume of water in the cylinder when it is full
= πr2h
= π × 3 × 3 × 6
= 54π cm3
Volume of water displaced = Volume of cone + Volume of hemisphere
= `1/3 pir^2h + 2/3 pir^3`
= `1/3 pir^2 (h + 2r)`
= `1/3 pi xx 2 xx 2(4 + 2 xx 2)`
= `1/3 pi xx 4 xx 8`
= `32/3 pi cm^3`
Therefore, volume of water which is left
= `54 pi - 32/3 pi`
= `130/3 pi cm^3`
= `130/3 xx 22/7 cm^3`
= `2860/21 cm^3`
= 136.19 cm3
= 136 cm3
संबंधित प्रश्न
A model of a ship is made to a scale 1: 300
1) The length of the model of the ship is 2 m. Calculate the lengths of the ship.
2) The area of the deck ship is 180,000 m2. Calculate the area of the deck of the model.
3) The volume of the model in 6.5 m3. Calculate the volume of the ship.
Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed.
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate:
- the radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
The surface area of a sphere is 5544 `cm^2`, find its diameter.
The dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of painting it at the rate of Rs. 2 per sq. m.
If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre.
The radius of a sphere is 10 cm. If we increase the radius 5% then how many % will increase in volume?
