Advertisements
Advertisements
Question
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.
Options
1 : 4
1 : 3
2 : 3
2 : 1
Advertisements
Solution
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is 1 : 4.
Explanation:
Given that radius of a hemispherical balloon (r1) = 6 cm
Since, air is pumped into balloon.
Then, radius of hemispherical balloon (r2) = 12 cm
∴ Ratio of the surface areas of the balloon in both cases = `(3pir_1^2)/(3pir_2^2)`
`\implies r_1^2/r_2^2 = (6)^2/(12)^2`
= `36/144`
= `1/4`
= 1 : 4
Hence, ratio of the surface areas of the balloon in the two cases is 1 : 4.
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of radius 14 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of diameter 14 cm.
`["Assume "pi=22/7]`
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.
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]`
On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:
1) the actual length of the diagonal distance AC of the plot in km.
2) the actual area of the plot in sq. km.
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.
Find the surface area of a sphere of radius 10.5 cm.
The surface area of a sphere is 5544 `cm^2`, find its diameter.
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?
A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
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 radius of the solid sphere.
- the number of cones recast. [Take π = 3.14]
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
Find the total surface area of a hemisphere of radius 10 cm.
The total surface area of a hemisphere of radius r is
A sphere and a cube are of the same height. The ratio of their volumes 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 ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
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
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.
