Advertisements
Advertisements
Question
A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder .
Solution
Radius of the solid cylinder (r) = 2 cm
Height of cylinder (h) = 45 cm
Volume of cylinder = `pir^2h`
= `22/7 xx 2 xx 2 xx 45`
= `3960/7` cm3
Diameter of metallic sphere = 6 cm
Therefore, Radius (r1) = 3 cm
Volume of sphere = `4/3pi(r1)^3`
= `4/3 xx 22/7 xx 3 xx 3 xx 3`
= `792/7`cm3
Therefore, No. of spheres = `3960/7 + 792/7 = 5`
Number of spheres that can be made = 5
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]
Find the surface area of a sphere of diameter 21 cm .
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 dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of
painting it at the rate of Rs. 2 per sq. m.
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere?
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
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.
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?
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.
A sphere and a cube are of the same height. The ratio of their volumes is
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 cone and a hemisphere have equal bases and equal volumes the ratio of their heights is
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
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]
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.
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.
