Answer to Question #269836 in Geometry for justt

Question

a triangle has sides that measures 15 cm, 20 cm, and 25 cm. find the exact volume of the solid of revolution formed when the triangle is revolved about the side of length 25 cm.

Answer 1

The triangle is right angled

Solid of revolution will be a bicone

Using Hero's formula

Area if triangle A$=\sqrt{S(s-a)(s-b)(s-c)}$

Where a,b,c are sides of the triangle and S $=\frac{1}{2}(a+b+c)$

$A=\sqrt{30(30-15)(30-25)(30-20)}$

$=150cm^2$

Height, h of the triangle with $25cm$ as base is given by;

$\frac{1}{2}×25×h=150$

$h=12cm$

The solid of revolution formed is a bicone

Volume of cone $=\frac{1}{3}\pi\>r^2h$ where

$r=$ Radius

h= height of cone

Volume of the bicone ;

$\frac{1}{3}\pi×12^2(h_1)+\frac{1}{3}\pi×12^2(h_2)$

$=\frac{1}{3}\pi×12^2(h_1+h_2)$

$=\frac{1}{3}\pi×12^2×25$

$=3769.9cm^2$