Advertisements
Advertisements
Question
The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?
Solution
Let the diameter of the earth be d. Therefore, the radius of the earth will be `d/2`.
The diameter of the moon will be `d/4`, and the radius of the moon will be `d/8`.
Volume of the moon = `4/3pir^3=4/3pi(d/8)^3=1/512xx4/3pid^3`
Volume of the earth = `4/3pi^3=4/3pi(d/2)^3=1/8xx4/3pid^3`
`"Volume of the moon"/"Volume of the earth"` = `(1/512xx4/3pid^3)/(1/8xx4/3pid^3) = 1/64`
⇒ Volume of the moon = `1/64 "Volume of the earth"`
Therefore, the volume of the moon is `1/64` of the volume of the earth.
APPEARS IN
RELATED QUESTIONS
Find the volume of a sphere whose radius is 0.63 m.
`["Assume "pi=22/7]`
Find the volume of a sphere whose surface area is 154 cm2.
`["Assume "pi=22/7]`
A cylinder whose height is two thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.
The diameter of a coper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.
A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?
If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.
The volume (in cm3) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r units.
A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is ______.
Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.
