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Let h 1 be the height of x and h2 be the height of y. The diameters of two cones are equal. If their slant heights are in the ratio , find the ratio of their curved surface areas. There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. Find the ratio of their radii. According to given condition:. A heap of wheat is in the form of a cone of diameter Find its volume. How much cloth is required to just cover the heap?
Find what length of canvas, 1. Also, find the cost of the canvas at the rate of Rs. Canvas required for stitching and folding. Total canvas required area. Length of canvas. Total cost. A solid cone of height 8 cm and base radius 6 cm is melted and re-casted into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.
Volume of smaller cone. Number of cones so formed. The total surface area of a right circular cone of slant height 13 cm is. The area of the base of a conical solid is 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 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? On submerging six equal solid cones into it, one-fourth of the water overflows. Therefore, volume of the equal solid cones submerged. Now, volume of each cone submerged. The volume of a conical tent is m 3 and the area of the base floor is m 2. Calculate Ch 1 Class 10 Maths Icse Github the:. Hence, radius of the base of the conical tent i. The surface area of a sphere is cm 2 , find its volume. The volume of a sphere is cm 3 ; find its diameter and the surface area.
A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made? How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm. Calculate the radius of the new sphere. The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their:. If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in the volume, what is the diameter of the sphere?
Let r be the radius of the sphere. According to the condition:. A solid metal sphere is cut through its centre into 2 equal parts. If the diameter of the sphere is find the total surface area of each part correct to 2 decimal places. The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively.
A solid sphere and a solid hemi-sphere have the same total surface area. Find the ratio between their volumes. Let the radius of the sphere be 'r 1 '.
Let the radius of the hemisphere be 'r 2 '. Dividing V 1 by V 2 ,. Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and recasted into a single solid sphere. Let radius of the larger sphere be 'R'. Volume of single sphere. Surface area of the sphere. Find the percentage increase in its:. Let the radius of the sphere be 'r'. Total surface area the sphere, S. New surface area of the sphere, S'.
Percentage change in radius. Let the new volume of the sphere be V'. A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2. Calculate the number of cones recast. A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cone of height 32 cm. Volume of spherical shell. Volume of solid circular cone. Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm.
Let the radius of the smaller cone be 'r' cm. Volume of larger cone. A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere. Let r be the radius of sphere. A hemi-spherical bowl of internal radius 9 cm is full of liquid.
This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl? A hemispherical bowl of diameter 7. This sauce is poured into an inverted cone of radius 4. Find the height of the cone if it is completely filled.
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0. Find the number of spheres formed. Volume of a cone. The total area of a solid metallic sphere is cm 2. It is melted and recast into solid right circular cones of radius 2. Number of cones. A solid metallic cone, with radius 6 cm and height 10 cm, is made of some heavy metal A. In order to reduce 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 the metal A to the volume of metal B in the solid. Volume of the whole cone of metal A. Volume of the cone with metal B. A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones. Let the number of small cones be 'n'.
Volume of small spheres. The surface area of a solid metallic sphere is cm 2. It is melted and recast into solid right circular cones of radius 3. Calculate :. A cone of height 15 cm and diameter 7 cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed. A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of the hemisphere.
The radius of the base of the cone is 3. Calculate the height of the cone and the surface area of the buoy, correct to two decimal places. From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Area of circular base. Area of curved surface area of cone. Surface area of remaining part. The cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.
The diameter of the largest hemisphere that can be placed on a face of a cube of side 7 cm will be 7 cm. A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of the top which is open is 5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.
Find the number of lead shots dropped in the vessel. Therefore, No. A hemispherical bowl has negligible thickness and the length of its circumference is cm.
Let r be the radius of the bowl. Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm. Volume of the cone. The radii of the bases of two solid right circular cones of same height are r 1 and r 2 respectively. The cones are melted and recast into a solid sphere of radius R. Find the height of each cone in terms r 1 , r 2 and R.
Let the height of the solid cones be 'h'. Volume of solid circular cones. 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. Volume of the solid hemisphere. Volume of 1 cone. A cone and a hemisphere have the same base and same height. Let the radius of base be 'r' and the height be 'h'. Volume of cone, V c.
Volume of hemisphere, V h. From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base are removed. Find the volume of the remaining solid. Volume of the remaining part.
From a solid cylinder whose height is 16 cm and radius is 12 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume and total surface area of the remaining solid. A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is m and its slant height is 80 m, calculate the total area of canvas required. Also, find the total cost of canvas used at Rs 15 per meter if the width is 1.
Total cost of canvas at the rate of Rs 15 per meter. A circus tent is cylindrical to a height of 8 m surmounted by a conical part. If total height of the tent is 13 m and the diameter of its base is 24 m; calculate:. A cylindrical boiler, 2 m high, is 3. It has a hemispherical lid.
Find the volume of its interior, including the part covered by the lid. A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is and the diameter of hemisphere is 3. Calculate the capacity and the internal surface area of the vessel. A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside.
A cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm 14 cm Spherical marbles of diameter 1. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.
Volume of one ball. The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel excluding the floor at the rate of Rs 2. Internal surface area of the tunnel. Therefore, total expenditure. The horizontal cross-section of a water tank is in the shape of a rectangle with semicircle at one end, as shown in the following figure.
The water is 2. Calculate the volume of water in the tank in gallons. Therefore, Volume of water filled in gallons. The given figure shows the cross-section of a water channel consisting of a rectangle and a semicircle. Assuming that the channel is always full, find the volume of water discharged through it in one minute if water is flowing at the rate of 20 cm per second.
Give your answer in cubic meters correct to one place of decimal. Flow of water in one minute at the rate of 20 cm per second. An open cylindrical vessel of internal diameter 7 cm and height 8 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is cm and height 8 cm. Find the volume of water required to fill the vessel. If this cone is replaced by another cone, whose height is cm and radius of whose base is 2 cm, find the drop in the water level.
Volume of the cylinder. On placing the cone into the cylindrical vessel, the volume of the remaining portion where the water is to be filled. Therefore, volume of new cone. Let h be the height of water which is dropped down. A cylindrical can, whose base is horizontal and of radius 3.
One trial of this experiment has two possible outcomes: Heads H or Tails T. So for an individual toss, it has only one outcome, i. The sum of the probabilities of all the elementary events of an experiment is one.
Example: take the coin-tossing experiment. An event that has no chance of occurring is called an Impossible event , i. As 7 can never be an outcome of this trial. The probability of occurrence of a sure event is one. The range of probability of an event lies between 0 and 1 inclusive of 0 and 1, i. Geometric probability is the calculation of the likelihood that one will hit a particular area of a figure.
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