Advertisements
Advertisements
प्रश्न
A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone is
विकल्प
4 cm
5 cm
6 cm
8 cm
उत्तर
Volume of cylinder `=pir^2h = pi xx (8)^2 xx 2= 128 pi cm^2`
Let r be the radius of cone
But,
The volume of cone = volume of cylinder
`1/3 pi r^2 h = 128pi`
`r^2 = (128 xx 3)/6 = 64`
r = 8 cm
Hence, Radius of cone = 8 cm.
APPEARS IN
संबंधित प्रश्न
A container open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends, as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container. at the rate of 21 per litre. [use π=22/7]
A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained is drawn into a wire of diameter 1/16 cm, find the length of the wire [use π=22/7]
A cone of height 20 cm and radius of base 5 cm is made up of modeling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.
A solid toy s in the form of a hemisphere surrounded by a right circular cone . The height of cone is 4 cm and the diameter of the base is 8 cm . Determine the volume of the toy. If a cube circumscribes the toy , then find the difference of the volumes of cube and the toy .
A frustum of a cone is 9 cm thick and the diameters of its circular ends are 28 cm and 4 cm. Find the volume and lateral surface area of the frustum.
(Take π = 22/7).
If a cone and a sphere have equal radii and equal volumes. What is the ratio of the diameter of the sphere to the height of the cone?
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.
A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm, respectively. Find
- the volume of water which can completely fill the bucket;
- the area of the metal sheet used to make the bucket.
A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm and radii of its lower and upper ends are 8 cm and 20 cm, respectively. Find the cost of the bucket if the cost of metal sheet used is Rs 15 per 100 cm2.
A solid metallic right circular cone 20 cm high and whose vertical angle is 60°, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter `1/12` cm, then find the length of the wire.
