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
APPEARS IN
RELATED QUESTIONS
Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed.
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate:
- the radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
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 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 Rs. 4 per 100 `cm^2`
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]
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is
A hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: the volume of remaining solid
A conical tent is to accommodate 77 persons. Each person must have 16 m3 of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
