Advertisements
Advertisements
Question
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
Solution
(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
RELATED QUESTIONS
Find the surface area of a sphere of radius 10.5 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of diameter 3.5 m.
`["Assume "pi=22/7]`
Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm2.
`["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]`
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.
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 10.5 cm.
A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?
How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 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.
The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.
Calculate:
- its volume,
- the surface area of the tunnel (excluding the floor) and
- its floor area.
Find the total surface area of a hemisphere of radius 10 cm.
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
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 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 .
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find volume of material of the vessel.
The cylinder of radius 12 cm have filled the 20 cm with water. One piece of iron drop in the stands of water goes up 6.75 cm. Find the radius of sphere piece.
