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 diameter 21 cm.
`["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.
Find the surface area of a sphere of radius 5.6 cm.
The surface area of a sphere is 2464 cm2, find its volume.
Find the total surface area of a hemisphere of radius 10 cm.
The total surface area of a hemisphere of radius r 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
Find the radius of a sphere whose surface area is equal to the area of the circle of diameter 2.8 cm
Find the volume of the hollow sphere whose inner diameter is 8 cm and the thickness of the material of which it is made is 1 cm .
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]
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 given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown.

Calculate :
- the total surface area.
- the total volume of the solid and
- the density of the material if its total weight is 1.7 kg.
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.
The volume of a sphere is 905 1/7 cm3, find its diameter.
There is surface area and volume of a sphere equal, find the radius of sphere.
A spherical cannon ball, 28 cm in diameter is melted and recast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone, correct to one place of decimal.
The radius of a sphere is 10 cm. If we increase the radius 5% then how many % will increase in volume?
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 ______.
