Question

Problem 11.1 A right triangle with hypotenuse 10 inches
and other two sides of variable length is rotated about its
longest side thus giving rise to a solid. Find the maximum
possible volume of such a solid.
(a) (250/3) in (b) (160/3), in
(c) 325/3nt in
(d) None of these
​

Answer 1

Answer:

The area of a right angled triangle with variable sides is maximum when the sides are equal.

Let the sides of this triangle = x

So, x^2 + x^2= 100

So, x = 5√2

Now, the triangle is rotated around its longest side, on its hypotenuse.

Lets divide the triangle into two triangles. Now draw a line from the midpoint of the hypotenuse to the opposite vertex.

Now, we get two identical triangles with two sides = 5 inches each and the other side = 5√2 inches.

Rotating the entire triangle is like rotating these two individual triangles.

So, we get two cones on top of each other.

So, total volume the solid would take = 2* (1/3) * pi * 5^2 * 5 = 0.67 * 125 * pi= 83.33 pi