Question

1. A solid object in the shape of a double cone is traced by rotating a right-angled triangle of smaller
sides 12 cm and 5 cm about the hypotenuse of the triangle. Find the cost (to the nearest rupee) of
painting its surface at the rate of 3.50 per cm?
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Answer 1

Step-by-step explanation:

The double cone so formed is made by revolving it around the hypotenuse.

And the hypotenuse is 13 cm.

Draw a perpendicular from B to AC, Let BD =h

So Area of ABC = 1/2 (12*5) = 30

And Area of ABC with base AC and height BD = 1/2(h*13) = 30

So h = 60/13

So BD is 60/13 cm.

The triangle ABC is rotated making axis as BD.

So the double cone formed will be has the figure as :

So area of ABB' + area of BCB' is the reqired area.

And BD is the radius = 60/13

So the area =π(AB×BD) + π(BC×BD)=π(12×6013) +π(5×6013)=246.59cm2And the rate is given as 3.50/cm2So the total cost =246.59×3.50 = 863.06Rs

sorry for bad drawings

hope this helps