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On the base edge of the metallic plate, which is in the form of a right triangle is soldered to a wire. The wire is rotated around its own axis. What is the maximum volume that can be generated by a metallic plate given that the smallest side of the triangular plate is 10 cm and the largest side is 4 cm greater than the second largest side?

On the base edge of the metallic plate, which is in the form of a right triangle is soldered to a wire. The wire is rotated around its own axis. What is the maximum volume that can be generated by a metallic plate given that the smallest side of the triangular plate is 10 cm and the largest side is 4 cm greater than the second largest side? Correct Answer 367.5π

Given:

The smallest side of the triangular plate = 10 cm

Largest side is 3 cm greater than the second largest side

Formula used:

Volume of cone = 1/3πr2h

Calculation used:

Let the second largest side be x than other two sides be 10 and (x + 4)

⇒ (10)2 + x2 = (x + 4)2

⇒ 100 + x2 = x2 + 8x + 16

⇒ 100 – 16 = 8x

⇒ 84 = 8x

⇒ x = 84/8 = 21/2

Volume generated will be maximum if the larger side serves as the base radius of the cone, which actually is the volume generated in the above process.

∴ Maximum volume = 1/3 π × (21/2)210 = 367.5π (approx.)

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