Advertisements
Advertisements
Question
Find the volume of a sphere, if its surface area is 154 sq.cm.
Advertisements
Solution
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
RELATED QUESTIONS
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of radius 14 cm.
`["Assume "pi=22/7]`
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 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.
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 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`.
The diameter of the moon is approximately one fourth of the diameter of the earth. Find the
ratio of their surface areas.
The surface area of a sphere is 2464 cm2, find its volume.
The volume of a sphere is 38808 cm3; find its diameter and the surface area.
What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?
A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid.
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.
Find the volume of a sphere whose surface area is 154 cm2.
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 largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
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 radius of the sphere whose surface area is equal to its volume .
Find the volume of the hollow sphere whose inner diameter is 8 cm and the thickness of the material of which it is made is 1 cm .
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.
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 given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown.
Calculate :
- the total surface area.
- the total volume of the solid and
- the density of the material if its total weight is 1.7 kg.
Find the volume and surface area of a sphere of diameter 21 cm.
The volume of a sphere is 905 1/7 cm3, find its diameter.
There is surface area and volume of a sphere equal, find the radius of sphere.
A spherical cannon ball, 28 cm in diameter is melted and recast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone, correct to one place of decimal.
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
The radius of a sphere is 10 cm. If we increase the radius 5% then how many % will increase in volume?
The cylinder of radius 12 cm have filled the 20 cm with water. One piece of iron drop in the stands of water goes up 6.75 cm. Find the radius of sphere piece.
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.
