Advertisements
Advertisements
प्रश्न
A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
विकल्प
4
3
6
8
Advertisements
उत्तर
In the given problem, we have a cylindrical rod of the given dimensions:
Radius of the base (rc) = x units
Height of the cylinder (h) = 8x units
So, the volume of the cylinder (Vc) = ` pi r^2 h`
`= pi x^2 (8x) `
`= 8 pi x^3`
Now, this cylinder is remolded into spherical balls of same radius. So let us take the number of balls be y.
Total volume of y spheres (Vs) = `y(4/3 pi r^3) `
=`y(4/3 pi x^3)`
So, the volume of the cylinder will be equal to the total volume of y number of balls.
We get, `V_c = yV_s`
`8 pi x^3 = y (4/3 pi x^3)`
` 8 = 4/3 y`
` y = ((8)(3))/4`
y = 6
Therefore, the number of balls that will be made is 6 .
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of diameter 3.5 m.
`["Assume "pi=22/7]`
Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]
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.
On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:
1) the actual length of the diagonal distance AC of the plot in km.
2) the actual area of the plot in sq. km.
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 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.
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.
Calculate:
- its volume,
- the surface area of the tunnel (excluding the floor) and
- its floor area.
Find the radius of a sphere whose surface area is 154 cm2.
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is
A hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
Find the volume of a sphere, if its surface area is 154 sq.cm.
A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder .
From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: the weight of the material drilled out if it weighs 7 gm per cm3.
The volume of a sphere is 905 1/7 cm3, find its diameter.
There is surface area and volume of a sphere equal, find the radius of sphere.
A solid sphere is cut into two identical hemispheres.
Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.
Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.
Which of the following is valid?
