Advertisements
Advertisements
Question
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 number of cones recast. `("Take" pi =22/7)`
Solution
∴ R = 14 cm
Volume of sphere melted = `4/3 pi "R"^3`
`= 4/3 xx pi xx 14 xx 14 xx 14`
Radius of each cone recasted = r = 3.5 cm
Height of each cone recasted = h = 7 cm
∴ Volume of each cone recasted = `1/3 pi "r"^2"h"`
`= 1/3 xx pi xx 3.5 xx 3.5 xx 7`
∴ Number of cones recasted = `"Volume of sphere melted"/"Volume of each cone formed"`
`= (4/3 xx pi xx 14 xx 14 xx 14)/(1/3 xx pi xx 3.5 xx 3.5 xx 7)`
= 128
APPEARS IN
RELATED QUESTIONS
A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
`["Assume "pi = 22/7]`
A right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
Find the surface area of a sphere of radius 10.5 cm .
Find the surface area of a sphere of diameter 14 cm .
Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and recasted into a single solid sphere. Taking π = 3.1, find the surface area of the solid sphere formed.
A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid.
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.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
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
If the surface area of a sphere is 144π m2, then its volume (in m3) is
Find the surface area and volume of sphere of the following radius. (π = 3.14)
4 cm
Find the radius of the sphere whose surface area is equal to its volume .
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown.
Calculate :
- the total surface area.
- the total volume of the solid and
- the density of the material if its total weight is 1.7 kg.
A conical tent is to accommodate 77 persons. Each person must have 16 m3 of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.
There is a ratio 1: 4 between the surface area of two spheres, find the ratio between their radius.
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
The radius of a sphere is 10 cm. If we increase the radius 5% then how many % will increase in volume?
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.
