Question

a right angle 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 cone so formed is​

Answer 1

Answer:

Step-by-step explanation:

We know that a : b = 3 : 4

a = 3 k, b = 3 k

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 = 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.