Advertisements
Advertisements
Question
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
Advertisements
Solution
Let the radius of the sphere be r cm.
Volume of the sphere (V) = 38808 cm3
Volume of the sphere (V) = `4/3πr^3`
⇒ 38808 = `4/3 xx 22/7 xx r^3`
⇒ r3 = `[38808 xx21]/88` = 9261
⇒ r3 = 9261
⇒ r3 = `root3(9261)`
⇒ r = 21 cm
∴ Surface area of the sphere = 4πr2
= `4 xx 22/7 xx (21)^2`
= 5544 cm2
Thus, the surface area of the sphere is 5544 cm2.
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of diameter 14 cm.
`["Assume "pi=22/7]`
Find the radius of a sphere whose surface area is 154 cm2.
`["Assume "pi=22/7]`
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.
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 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.
Find the surface area of a sphere of radius 10.5 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.
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.
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.
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.
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r 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.
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.
Find the volume of a sphere whose surface area is 154 cm2.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
The total surface area of a hemisphere of radius r is
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube 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
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
Find the surface area and volume of sphere of the following radius. (π = 3.14)
4 cm
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 .
A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?
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]
Find the volume and surface area of a sphere of diameter 21 cm.
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
The total surface area of a hemisphere is how many times the square of its radius
A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm3 of ball bearings. Find the:
- maximum number of ball bearings that each box can have.
- mass of each box of ball bearings in kg.
(Use π = `22/7`)
