9514 1404 393
Answer:
1200 ≈ 3769.9 cubic units
Explanation:
The area of the triangle is given by Heron's formula:
s = (16 +25 +39)/2 = 40
A = √(s(s -16)(s -25)(s -39)) = √14400 = 120
Then the height is ...
A = 1/2·bh
h = 2A/b = 2(120)/16 = 15
The centroid of the triangle is located 15/3 = 5 units from the axis of rotation, so it will be rotated through a circle with a circumference of ...
C = 2πr = 10π . . . units
The volume is the product of this distance and the area of the triangle, so is ...
V = CA = (10π)(120) = 1200π . . . cubic units
The solid's volume is 1200π ≈ 3769.9 cubic units.