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]`
Find the surface area of a sphere of radius 14 cm.
`["Assume "pi=22/7]`
Find the radius of a sphere whose surface area is 154 cm2.
`["Assume "pi=22/7]`
A model of a ship is made to a scale 1: 300
1) The length of the model of the ship is 2 m. Calculate the lengths of the ship.
2) The area of the deck ship is 180,000 m2. Calculate the area of the deck of the model.
3) The volume of the model in 6.5 m3. Calculate the volume of the ship.
Find the surface area of a sphere of diameter 3.5 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.
A hemi-spherical dome of a building needs to be painted. If the circumference of the base of
the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00
`cm^2`
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.
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.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
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 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 conical tent is to accommodate 77 persons. Each person must have 16 m3 of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.
