Advertisements
Advertisements
Question
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
Options
4
3
6
8
Advertisements
Solution
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
RELATED QUESTIONS
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 wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base
of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100
`cm^2`.
If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere?
The surface area of a solid sphere is increased by 12% without changing its shape. Find the percentage increase in its:
- radius
- volume
A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.
What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?
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.
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?
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.
There is a ratio 1: 4 between the surface area of two spheres, find the ratio between their radius.
The total surface area of a hemisphere is how many times the square of its radius
