Q. 314.0( 10 Votes )

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Answer :


When a right-angled triangle is revolved around its hypotenuse, a double cone is formed with same radius but with different heights.


Given,


AB = 15 cm


AC = 20 cm


Let, OB = x and OA = y


Observe from the figure,


In right-angled triangle ABC, By Pythagoras theorem [Hypotenuse2 = Base2 + Perpendicular2]


BC2 = AC2 + AB2


BC2 = 202 + 152


BC2 = 400 + 225


BC2 = 625


BC = 25 cm


In ΔOAB


AB2 = OA2 + OB2


152 = x2 + y2 ……[1]


In ΔAOC


AC2 = OA2 + OC2


202 = y2 + (BC – OB)2


400 = y2 + (25 – x)2


400 = y2 + 625 – 50x + x2


400 = 152 + 625 – 50x


400 = 225 + 625 – 50x


50x = 450


x = 9 cm


Putting in [1], we get


152 = 92 + y2


y2 = 225 – 81


y2 = 144


y = 12 cm


Also, OC = 25 – x = 25 – 13 = 12 cm2


Now, Volume of cone


Where r denotes base radius and h denotes height of cone


Hence, volume of double cone




Curved surface area of cone = πrl


Where r denotes base radius and l denotes slant height


Also,


Surface area of double cone = CSA of left cone + CSA of right cone


Putting values,


Surface area = π(OA)(AB) + π(OA)(AC)


= 3.14 × 12 × (15 + 20)


= 1318.8 cm2


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