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 5.6 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.
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`)
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
The surface area of a sphere is 5544 `cm^2`, find its diameter.
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`
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.
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.
Find the radius of a sphere whose surface area is 154 cm2.
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
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
Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m.
A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere .
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 sphere is cut into two identical hemispheres.
Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.
Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.
Which of the following is valid?
