Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Radius (r1) of spherical balloon = 7 cm
Radius (r2) of the spherical balloon, when air is pumped into it = 14 cm
Required ratio = `"Initial surface area"/"Surface area after pumping air into a balloon"`
= `(4pir_1^2)/(4pir_2^2)` = `(r_1/r_2)^2`
= `(7/14)^2` = `1/4`
Therefore, the ratio between the surface areas in these two cases is 1 : 4.
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 diameter 21 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.
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.
Find the surface area of a sphere of radius 10.5 cm.
Find the surface area of a sphere of diameter 21 cm.
A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base
of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100
`cm^2`.
The surface area of a solid sphere is increased by 12% without changing its shape. Find the percentage increase in its:
- radius
- volume
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
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.
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 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]
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
A sphere cut out from a side of 7 cm cubes. Find the volume of this sphere?
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.
