SOLUTION: 1. The volume of a regular triangular prism is 240 square root of 3 cu In. and its altitude is 15 in. Find the side of the base

Algebra ->  Rectangles -> SOLUTION: 1. The volume of a regular triangular prism is 240 square root of 3 cu In. and its altitude is 15 in. Find the side of the base      Log On


   

Question 1146136: 1. The volume of a regular triangular prism is 240 square root of 3 cu
In. and its altitude is 15 in. Find the side of the base
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. The volume of a regular triangular prism is 240 square root of 3 cu
In. and its altitude is 15 in.
Find the side of the base
:
Assuming the base triangle is a equilateral triangle
let s = the side of the base
Find the height of the base triangle
h = sqrt%28s%5E2-%28.5s%29%5E2%29
h = sqrt%28s%5E2-.25s%5E2%29
h = sqrt%28.75s%5E2%29
Find the area of the base triangle
A = 1%2F2s*h
Replace h
A = 1%2F2s%2Asqrt%28.75s%5E2%29
extract s
A = 1%2F2s%5E2%2Asqrt%28.75%29
volume (240) is the area of the base * the altitude (15)
1%2F2s%5E2%2Asqrt%28.75%29%2A15 = 240sqrt%283%29
get rid of the fraction, mult by 2
s%5E2%2Asqrt%28.75%29%2A15 = 480sqrt%283%29
divide both sides by 15
s%5E2%2Asqrt%28.75%29 = 32sqrt%283%29
square both sides
s%5E4%2A.75 = 1024*3
s%5E4%2A.75 = 3072
divide both sides by .75
s%5E4 = 4096
Use your calc to find the 4th root of 4096
s = 8 inches is the side of the base