Advertisements
Advertisements
प्रश्न
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
उत्तर
Height of cone = 8 cm
Radius = 5 cm
Volume = `1/3pir^2h`
= `1/3 xx 22/7 xx 5 xx 5 xx 8 cm^3`
= `4400/21 cm^3`
Therefore, volume of water that flowed out
= `1/4 xx 4400/21 cm^3`
= `1100/21 cm^3`
Radius of each ball = 0.5 cm = `1/2` cm
Volume of a ball = `4/3pir^3`
= `4/3 xx 22/7 xx 1/2 xx 1/2 xx 1/2 cm^3`
= `11/21 cm^3`
Therefore, No. of balls = `1100/21 ÷ 11/21 = 100`
Hence, number of lead balls = 100
संबंधित प्रश्न
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
`["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 Joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.
The circumference of the base of a 10 m height conical tent is 44 metres. Calculate the length of canvas used in making the tent if width of canvas is 2 m. (Use it 𝜋= 22/7).
A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius of each is to the height of each as 3:4.
Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.
Monica has a piece of Canvas whose area is 551 m2. She uses it to have a conical tent made, with a base radius of 7m. Assuming that all the stitching margins and wastage incurred while cutting, amounts to approximately 1 m2. Find the volume of the tent that can be made with it.
The circumference of the base of a 12 m high conical tent is 66 m. Find the volume of the air contained in it.
A solid sphere and a solid hemi-sphere have the same total surface area. Find the ratio between their volumes.
A solid metallic cone, with radius 6 cm and height 10 cm, is made of some heavy metal A. In order to reduce its weight, a conical hole is made in the cone as shown and it is completely filled with a lighter metal B. The conical hole has a diameter of 6 cm and depth 4 cm. Calculate the ratio of the volume of metal A to the volume of the metal B in the solid.
A solid metallic hemisphere of diameter 28 cm is melted and recast into a number of identical solid cones, each of diameter 14 cm and height 8 cm. Find the number of cones so formed.
A cone and a hemisphere have the same base and the same height. Find the ratio between their volumes.
A solid is in the form of a right circular cone mounted on a hemisphere. The diameter of the base of the cone, which exactly coincides with hemisphere, is 7 cm and its height is 8 cm. The solid is placed in a cylindrical vessel of internal radius 7 cm and height 10 cm. How much water, in cm3, will be required to fill the vessel completely?
What will be the cost of making a closed cone of tin sheet having radius of base 6 m and slant height 8 m if the rate of making is Rs.10 per sq.m? `(π = 22/7)`
Find the curved surface area of a cone whose height is 8 cm and base diameter is 12 cm .
The heights of two cones are in the ratio 1:3 and their base radii are in the ratio 3:1. Find the ratio of their volumes.
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown. Calculate: the density of the material if its total weight is 1.7 kg
The radius and height of cone are in the ratio 3 : 4. If its volume is 301.44 cm3. What is its radius? What is its slant height? (Take π = 3.14)
The ratio of the radii of two right circular cones of the same height is 1 : 3. Find the ratio of their curved surface area when the height cone is 3 times the radius of the smaller cone.
