BC² = 15² + 20²

BC² = 225 + 400 = 625

BC = 625 = 25 cm.

Let OA = x and OB = y.

In triangles ABO and ABC, we have BOA = BAC and ABO = ABC

So , by angle - angle - criterion of similarity, we have DBOA ~ DBAC

Therefore, BO/BA = OA/OC = BA/BC

—> y/15 = x/20 = 15/25

—> y/15 = x/20 = 3/5

—> y/15 = 3/5 and x = x 3/5

—> y = 3/5 × 15 and x = 3/5 × 20

—> y = 9 and x = 12

Thus, we have

OA = 12 cm and OB = 9cm

Also OC = BC - OB = 25 - 9 = 16 cm

When the ABC is revolved about the hypotenuse. we get a double cone as shown in figure.

Volume of the double cone = volume of the cone CAA’ + volume of the cone BAA’

= 1/3 π(OA)₂ × OC + 1/3 π(OA)² × OB

= 1/3 π× 12² 16 + 1/3 π×12² × 9

= 1/3 π×144(16+9)

= 1/3 ×3.14 × 144 × 25cm³

= 3768 cm³