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 total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]
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]`
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 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.
Find the surface area of a sphere of radius 14 cm.
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
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?
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 total surface area of a hemisphere of radius 10 cm.
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
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.
Find the surface area and volume of sphere of the following radius. (π = 3.14)
4 cm
How many lead balls of radii 1 cm each can be made from a sphere of 8 cm radius?
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)`
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 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.
