Advertisements
Advertisements
प्रश्न
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 ______.
विकल्प
1 : 4
1 : 3
2 : 3
2 : 1
Advertisements
उत्तर
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
संबंधित प्रश्न
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]`
Find the surface area of a sphere of diameter 14 cm.
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use 𝜋 = 3.14)
The dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of painting it at the rate of Rs. 2 per sq. m.
Assuming the earth to be a sphere of radius 6370 km, how many square kilo metres is area
of the land, if three-fourth of the earth’s surface is covered by water?
The volume of a sphere is 38808 cm3; find its diameter and the surface area.
A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.
Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere.
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
Find the radius of the sphere whose surface area is equal to its volume .
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]
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.
A vessel is in he form of an inverted cone. Its height is 11 cm., and the radius of its top which is open is 2.5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.25 cm., are dropped 2 into the vessel, `2/5`th of the water flows out. Find the number of lead shots dropped into the vessel.
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
