Advertisements
Advertisements
प्रश्न
If the surface area of a sphere is 144π m2, then its volume (in m3) is
विकल्प
288 π
316 π
300 π
188 π
Advertisements
उत्तर
In the given problem,
Surface area of a sphere = 144 π m2
So,
` 4 pi r^2 = 144 pi `
`r^2 = 144/4`
`r^2 = 36`
`r = sqrt(36)`
r = 6
Now, using the formula volume of the sphere, we get
`4/3 pi r^3 = 4/3 pi (6)^3`
` = 4/3 pi (216)`
`= 288 pi`
Therefore, volume of the sphere is `288 pi` .
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 right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
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.
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 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`.
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
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.
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.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
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 radius of the solid sphere.
- the number of cones recast. [Take π = 3.14]
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?
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.
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
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m.
From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: the weight of the material drilled out if it weighs 7 gm per cm3.
A vessel is in he form of an inverted cone. Its height is 11 cm., and the radius of its top which is open is 2.5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.25 cm., are dropped 2 into the vessel, `2/5`th of the water flows out. Find the number of lead shots dropped into the vessel.
