Advertisements
Advertisements
Question
Two cones have their heights in the ratio 1 : 3 and radii 3 : 1. What is the ratio of their volumes?
Solution
Let the radius of the cone is 3x and x,
And the height of the cone is y and 3y.
Then,
Volume of the first cone
`v_1 = 1/3 pir^2 h`
`=1/3 pi (3x)^2 y`
`=1/3 pi9x^2 y`
` = 3pix^2 y ............(1)`
Volume of the second cone
`v_2 = 1/3 pi(x)^2 xx 3y`
=`pix^2 y` ............... (2)`
Then the radius of their volume
`v_1/v_2 = (3pi x^2 y)/(pi x^2 y)`
Or
`v_1/v_2 = 3:1`
`v_1 :v_2 = 3:1`
APPEARS IN
RELATED QUESTIONS
A right triangle whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate.)
A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height and the base radius of the cone are also the same. Find the whole surface and volume of the remaining cylinder.
A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy. `[\text{Use}pi 22/7]`
A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8 : 5, determine the ratio of the radius of the base to the height of either of them.
The surface area of a sphere is 2464 cm2. If its radius be doubled, then what will be the surface area of the new sphere?
The total surface area of a cube is 864 cm2. Its volume is
How many solid cylinders of radius 6 cm and height 12 cm can be made by melting a solid sphere of radius 18 cm?
Activity: Radius of the sphere, r = 18 cm
For cylinder, radius R = 6 cm, height H = 12 cm
∴ Number of cylinders can be made =`"Volume of the sphere"/square`
`= (4/3 pir^3)/square`
`= (4/3 xx 18 xx 18 xx 18)/square`
= `square`
Tick the object which has more volume
A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of cube is ______.
Four horses are tethered with equal ropes at 4 corners of a square field of side 70 metres so that they just can reach one another. Find the area left ungrazed by the horses.
