Advertisements
Advertisements
Question
Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
Advertisements
Solution
Given, diameter of spherical marble = 1.4 cm
∴ Radius = `1.4/2` = 0.7 cm.
Volume of one ball = `4/3pir^3`
= `4/3pi (0.7)^3 cm^3` ...(i)
Diameter of beaker = 7 cm
∴ Radius = `7/2` cm,
Height of water (h) = 5.6 cm
∴ Volume of water = πr2h
= `pi (7/2 xx 7/2 xx 5.6) cm^3`
∴ Required No of balls dropped
= `(pi xx 49 xx 56 xx 3)/(4 xx 10 xx 4pi xx (0.7)^3)`
= `(49 xx 56 xx 3 xx 10 xx 10 xx 10)/(4 xx 10 xx 7 xx 7 xx 7 xx 4)`
= 150
RELATED QUESTIONS
Find the surface area of a sphere of diameter 21 cm.
`["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 areas.
A hemi-spherical dome of a building needs to be painted. If the circumference of the base of
the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00
`cm^2`
The volume of a sphere is 38808 cm3; find its diameter and the surface area.
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]
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.
A sphere and a cube are of the same height. The ratio of their volumes is
Find the radius of the sphere whose surface area is equal to its volume .
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 .
The total surface area of a hemisphere is how many times the square of its radius
