Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given, Radius of each cone and hemi-sphere (r) = 8 cm
Height of cone (h) = r = 8 cm
∴ Volume of solid
= `1/3pir^2h + 2/3pir^3`
= `1/3pir^2(h + 2r) cm^3`
= `1/3pi xx 8 xx 8(8 + 2 xx 8) cm^3`
= `64/3 pi(8 + 16) cm^3`
= `64/3pi xx 24`
= 512 π cm3
RELATED QUESTIONS
On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:
1) the actual length of the diagonal distance AC of the plot in km.
2) the actual area of the plot in sq. km.
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.
The surface area of a sphere is 5544 `cm^2`, find its diameter.
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is
If the surface area of a sphere is 2826 cm2 then find its volume. ( π= 3.14)
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 .
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 used.
A vessel is in he form of an inverted cone. Its height is 11 cm., and the radius of its top which is open is 2.5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.25 cm., are dropped 2 into the vessel, `2/5`th of the water flows out. Find the number of lead shots dropped into the vessel.
