Advertisements
Advertisements
Question
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
Solution
A volume of solid cone = `1/3 pir^2h = 1/3 xx 22/7 xx 5^2 xx 8 = 1/3 xx 22/7 xx 25 xx 8`
Volume of a small sphere = `4/3 pir^3 = 4/3 xx 22/7 xx (5/10)^3 = 4/3 xx 22/7 xx 125/1000`
Number of spheres formed = `"Volumeof cone"/"Volumeof sphere"` = `(1/3 xx 22/7 xx 25xx8)/(4/3 xx 22/7 xx 125/1000) = 400`
Thus 400 spheres are obtained by melting the solid cone.
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of diameter 14 cm.
`["Assume "pi=22/7]`
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
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`)
Find the surface area of a sphere of radius 10.5 cm .
Find the surface area of a sphere of radius 14 cm.
Find the surface area of a sphere of diameter 3.5 cm .
The surface area of a solid sphere is increased by 12% without changing its shape. Find the percentage increase in its:
- radius
- volume
A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere.
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.
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
Mark the correct alternative in each of the following:
In a sphere the number of faces 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`.
The model of a building is constructed with the scale factor 1 : 30.
(i) If the height of the model is 80 cm, find the actual height of the building in meters.
(ii) If the actual volume of a tank at the top of the building is 27m3, find the volume of the tank on the top of the model.
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
Find the radius of a sphere whose surface area is equal to the area of the circle of diameter 2.8 cm
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 surface area and volume of a sphere equal, find the radius of sphere.
There is a ratio 1: 4 between the surface area of two spheres, find the ratio between their radius.
The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
