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RIGHT CIRCULAR CONE, We see around us many objects such as an ice-cream cone, a conical vessel, a, clown's cap, etc. These objects are said to have the shape of a right circular, cone. In geometry, we define it as under., , RIGHT CIRCULAR CONE The solid generated by the rotation ofa right-angled triangle, about one of the sides containing the right angle is called a right circular cone., Thus, on rotating a right-angled triangular lamina, AOB about 0A, it generates a cone., The point A is the vertex of the cone., , Its base is a circle with centre O and radius OB., The length OA is the height of the cone and the length, AB is called its slant height., , Clearly, 2AOB, , =, , Cone, , 90"., , Ifradius ofthe base =runits, height= h units and slantheight=lunits, then, , P=(+), , I=VH+?., , Formulae:, For a right circular cone of radius = r units, height = h units and slant, , height= l units, we have:, (i) Slant height ofthe cone ), , = VH +r units., , (i) Volume of the cone = r h cubic units., (iii) Area of curved surface = (trl) sq units = (trVh* +r) sq units., , (iv) Total surface area = (area of the curved surface) + (area of the base), = (Ttrl + t r ) sq units = r(l+ r) sq units., , NOTE Takex = Sunless stated otherwise., , The height of a cone is 24 cm and the diameter of its base is 14 cm., , Find the stlant height, volume, area of curved surface and the total, surface area of the cone., SOLUTION, , Here, h = 24 cm and r = 7 cm., , Let the slant height be I cm. Then,, , l=Vi+r=V(24)*+(7)*, , =, , slant height =lcm = 25 cm., , /625 25., Cm, , B

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Volume of the cone=, , arh, x77, , -, , x, , 24)cm', , 1232 cm., Curved surface area of the cone= ard, , x7x 25)cm, , =550 cm?., , Total surface area ofthe cone = nr(l+r), , 7x(25+7, , cm, , 704 cm ., How manyy metres of cloth, 5 m wide, will be required to make a, conical tent, the radius of whose base is 7 m and height is 24 m?, SOLUTION, , Radius of the tent, r = 7m and its height, h = 24 m., , slant height, I =VP+* = /)*+ (24) m, = V625 m = 25 m., Area of the curved surface = (trl) sq units, , x7x 25 m, , Am, , B, , 550 m., Thus, the area of the cloth = 550m., , Length of the clothrequired=width5m=110 m., Hence, length of the cloth required is 110 m., , The height and the slamt height of a cone are 21 cm and 28 cm, respectively. Find the volume of the cone., SOLUTION, , We have, h = 21 cm and I = 28 cm., , P - + h r=/f-R* = /(28)*-(21* cm, r = / ( 2 8 + 2 1 ) X (28-21) cm = V49 X7 cm, , 7/7 cm., Volume of the, , cone=r'h, (22 x 343) cm = 7546 cm.