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
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.
Find the radius of a sphere whose surface area is 154 cm2.
`["Assume "pi=22/7]`
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
Find the surface area of a sphere of diameter 21 cm.
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 Rs. 4 per 100 `cm^2`
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 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 volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :
- radii,
- surface areas.
The surface area of a solid sphere is increased by 12% without changing its shape. Find the percentage increase in its:
- radius
- volume
A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.
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.
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
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 hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
9 cm
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
If the surface area of a sphere is 2826 cm2 then find its volume. ( π= 3.14)
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.
The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?
