Advertisements
Advertisements
प्रश्न
A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.
उत्तर
Diameter of sphere = 21 cm
Radius of sphere =`21/2` cm
Volume of sphere `= 4/3 pir^3 = (4xx21xx21xx21xx21pi)/(3xx2xx2xx2)= (21xx21xx21pi)/(3xx2) "cm"^3`
Diameter of the cone = 3.5 cm
Radius of the cone `= 3.5/2 = 7/4 "cm"`
Height = 3 cm
Volume of each cone` = 1/3pir^2h xx 1/3pixx3xx(7/4)^2 = (7/4)^2 pi "cm"^3 `
`"Total number of cones"= "Volume of sphere"/"Volume of a cone" = ((21xx21xx21pi)/(3xx2))/((7/4)^2pi) = (21xx21xx21xxpixx4xx4)/3xx2xxpixx)`
APPEARS IN
संबंधित प्रश्न
In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 3.5 cm. Find the total surface area of the bock `(Use pi=22/7)`
In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use `pi=22/7` and `sqrt5=2.236`)
In Fig. 5, from a cuboidal solid metallic block, of dimensions 15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block [Use
`pi=22/7`]
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2
[use `pi = 22/7`]
From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.
A cylindrical tub, whose diameter is 12 cm and height 15 cm is full of ice-cream. The whole ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice-cream cone ?
A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of `3/2` cm and its depth is `8/9 `cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.
A solid metal sphere of 6 cm diameter is melted and a circular sheet of thickness 1 cm is prepared. Determine the diameter of the sheet.
A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of the copper be 8.8 g per cm3, then find the weight of the wire.
Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.
Statement R( Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.
