A right angled triangle having hypotenuse 25 cm and sides are in the ratio 3:4 is made to revolve about its hypotenuse. The volume of the double cones of or med is

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CollectorBabu · Accepted Answer

Correct Answer: 1200 π cm 3. Given that, Hypotenuse is 25cm Sides are in ratio = 3:4 Lets say the sides are 3k and 4k, Then we will use the Pythagorean theorem: a² + b² = c² ( 3 k )² + ( 4 k )² = 25² 9 k² + 16 k² = 625 25 k² = 625, k² = 625 / 25 = 25, k = √ 25 = 5 cm Therefore: a = 3 · 5 = 15 cm, b = 4 · 5 = 20 cm. Area of the triangle: A = a b / 2 = 15 · 20 / 2 = 150 cm² Also: A = r · c / 2 = 150     (where r is the radius of both cones) r · 25 = 300, r = 300 : 25 r= 12 cm. The double cone has height: H = 25 cm, or it can be shown as: H1 + H2, where H 1 and H2 are heights of two cones. V = V1 + V2 = 1/3 r² π H1 + 1/3 r² π H2 = 1/3 r² π (H1 + H2 ) = 1/3 · 12² π · H = 1/3 · 144 π · 25 = 1200 π cm³ Answer: The volume of the double cone formed by revolving the triangle about its hypotenuse is 1200 π cm³.

A right angled triangle having hypotenuse 25 cm and sides are in the ratio 3:4 is made to revolve about its hypotenuse. The volume of the double cones of or med is

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