Advertisements
Advertisements
प्रश्न
Find the volume of a sphere, if its surface area is 154 sq.cm.
Advertisements
उत्तर
Let the radius of the sphere be r cm.
Surface area of the sphere = 154 cm2
∴ 4πr2 = 154 cm2
⇒ `4 xx 22/7 xx r^2` = 154
⇒ r2 = `[154 xx 7]/88`
⇒ r2 = 12.25
⇒ r2 = (3. 5)2
⇒ r = 3. 5
∴ Volume of the sphere = `4/3 πr^3`
= `4/3 xx 22/7 xx (3. 5)^3`
= 179.67 cm3
Thus, the volume of the sphere is 179.67 cm3.
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 certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.
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.
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
Find the surface area of a sphere of radius 10.5 cm.
Find the surface area of a sphere of radius 5.6 cm.
Find the surface area of a sphere of diameter 21 cm.
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use 𝜋 = 3.14)
The surface area of a sphere is 5544 `cm^2`, find its diameter.
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 hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
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]
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.
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.
Calculate:
- its volume,
- the surface area of the tunnel (excluding the floor) and
- its floor area.
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
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 of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.
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.
The ratio of the total surface area of a sphere and a hemisphere of same radius is
A sphere and a cube are of the same height. The ratio of their volumes is
A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
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
A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is
Find the surface area and volume of sphere of the following radius. (π = 3.14)
4 cm
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
If the surface area of a sphere is 2826 cm2 then find its volume. ( π= 3.14)
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 .
There is surface area and volume of a sphere equal, find the radius of sphere.
The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹ 0.14 per cm2
The total surface area of a hemisphere is how many times the square of its radius
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?
