Advertisements
Advertisements
प्रश्न
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
Advertisements
उत्तर
Let the radius of the be r
Surface area of the sphere = 4πr2 sq.units ...(1)
If the radius is increased by 25%
New radius = `25/100 xx "r" + "r"`
= `"r"/4 + "r"`
= `("r" + 4"r")/4`
= `(5"r")/4`
Surface area of the sphere
= `4pi((5"r")/4)^2"sq.units"`
= `4 xx pi xx (25"r"^2)/16`
= `(25pi"r"^2)/4"sq.units"`
Difference in surface area
= `(25pi"r"^2)/4 - 4pi"r"^2`
= `pi"r"^2(25/4 - 4)`
= `pi"r"^2((25 - 16)/4)`
= `pi"r"^2(9/4)`
= `(9pi"r"^2)/4`
Percentage of increase in surface area
= `"Difference in surface area"/"Old surface area" xx 100`
= `((9pi"r"^2)/4)/(4pi"r"^2) xx 100`
= `(9pi"r"^2)/(4 xx 4pi"r"^2) xx 100`
= `9/16 xx 100%` = 56.25 %
Percentage of increase in surface area = 56.25 %
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of radius 10.5 cm.
`["Assume "pi=22/7]`
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate:
- the radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
Find the surface area of a sphere of diameter 14 cm.
Find the surface area of a sphere of diameter 21 cm.
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.
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.
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
If the surface area of a sphere is 144π m2, then its volume (in m3) 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 and a hemisphere have equal bases and equal volumes the ratio of their heights is
If the surface area of a sphere is 2826 cm2 then find its volume. ( π= 3.14)
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m.
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 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 two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
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.
