Advertisements
Advertisements
Question
A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.
Solution
Height of solid cone (h) = 8 cm
Radius (r) = 6 cm
Volume of solid cone = `1/3pir^2h`
= `1/3 xx pi xx 6 xx 6 xx 8`
= 96π cm3
Height of smaller cone = 2 cm
And radius = `1/2` cm
Volume of smaller cone
= `1/3 xx pi xx 1/2 xx 1/2 xx 2`
= `1/6pi cm^3`
Number of cones so formed
= `(96pi)/(1/6pi)`
= `96pi xx 6/pi`
= 576
APPEARS IN
RELATED QUESTIONS
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
`["Assume "pi=22/7]`
A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is ₹ 12 per m2, what will be the cost of painting all these cones?
`("Use "π = 3.14" and take "sqrt1.04= 1.02)`
A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone.
The height of a cone is 21 cm. Find the area of the base if the slant height is 28 cm.
Find the total surface area of a right circular cone with radius 6 cm and height 8 cm.
The area of the curved surface of a cone is 60 cm2. If the slant height of the cone be 8 cm, find the radius of the base?
Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio 4 : 3.
The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surfaces.
The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use it 𝜋 = 3.14).
A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3:1.
The area of the base of a conical solid is 38.5 cm2 and its volume is 154 cm3. Find the curved surface area of the solid.
A vessel, in the form of an inverted cone, is filled with water to the brim. Its height is 32 cm and diameter of the base is 25.2 cm. Six equal solid cones are dropped in it, so that they are fully submerged. As a result, one-fourth of water in the original cone overflows. What is the volume of each of the solid cones submerged?
The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the:
- radius of the floor,
- height of the tent,
- length of the canvas required to cover this conical tent if its width is 2 m.
A solid metal sphere is cut through its center into 2 equal parts. If the diameter of the sphere is `3 1/2 cm`, find the total surface area of each part correct to two decimal places.
A solid sphere and a solid hemi-sphere have the same total surface area. Find the ratio between their volumes.
Surface area of a cone is 188.4 sq.cm and its slant height is 10 cm. Find its perpendicular height ( π= 3.14)
Volume of a cone is 1232 cm3 and its height is 24 cm. Find the surface area of the cone. `( π = 22/7)`
The radius and height of a cylinder, a cone and a sphere are same. Calculate the ratio of their volumes.
A buoy is made in the form of a hemisphere surmounted by a right circular cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is 3.5 m and its volume is two-third the volume of hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two decimal places.
