Advertisements
Advertisements
प्रश्न
The radius of a sphere is 10 cm. If we increase the radius 5% then how many % will increase in volume?
Advertisements
उत्तर
Volume of sphere = `4/3πr^3`
∴ Radius = r = 10 cm
∴ Volume of sphere = `4/3` π x 10 x 10 x 10
= `(4000π)/3` cm3
Now, increase the radius 5%
Radius of new sphere = `(10 xx 105)/100 = 21/2` cm.
Volume of new sphere = `4/3 π xx 21/2 xx 21/2 xx 21/2`
= `(9261π)/6` cm3
Increase volume = Volume of new sphere - Volume of sphere
= `(9261π)/6 - (4000π)/3`
= `(9261π - 8000π)/6`
= `(1261π)/6` cm
Percentage of increasing volume = `((1261π)/6 xx 100)/((4000π)/3)`
= `(1261π xx 100 xx 2)/(4000π xx 6)`
= `1261/80 %`
= `15 61/80 %`
संबंधित प्रश्न
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use 𝜋 = 3.14)
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`.
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 spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?
Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and recasted into a single solid sphere. Taking π = 3.1, find the surface area of the solid sphere formed.
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 sphere and a cube are of the same height. The ratio of their volumes is
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
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 volume of a sphere is 905 1/7 cm3, find its diameter.
