Advertisements
Advertisements
प्रश्न
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).
Advertisements
उत्तर
(i) Surface area of sphere = 4πr2
(ii) Height of cylinder = r + r = 2r
The radius of the cylinder = r
The curved surface area of cylinder = 2πrh
= 2πr (2r)
= 4πr2
(iii) Required ratio = `"Surface area of the sphere"/"Curved surface area of cylinder"`
= `(4pir^2)/(4pir^2)= 1/1`
Therefore, the ratio between these two surface areas is 1 : 1.
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of radius 10.5 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
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 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.
Find the surface area of a sphere of radius 5.6 cm.
Assuming the earth to be a sphere of radius 6370 km, how many square kilo metres is area
of the land, if three-fourth of the earth’s surface is covered by water?
A hemi-spherical dome of a building needs to be painted. If the circumference of the base of
the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00
`cm^2`
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.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
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.
A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere .
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 .
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate: the number of cones recasted [π = 3.14]
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.
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.
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
