SOLUTION: Given the surface area of a sphere is 40 pi cm^2, find its volume. And given that the area of an equilateral triangle is 67 cm^2, find its perimeter.

Algebra ->  Volume -> SOLUTION: Given the surface area of a sphere is 40 pi cm^2, find its volume. And given that the area of an equilateral triangle is 67 cm^2, find its perimeter.       Log On


   

Question 191520: Given the surface area of a sphere is 40 pi cm^2, find its volume.
And given that the area of an equilateral triangle is 67 cm^2, find its perimeter.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Given the surface area of a sphere is 40 pi cm^2, find its volume.
:
Two formulas: V = %284%2F3%29%2Api%2Ar%5E3 & SA = 4%2Api%2Ar%5E2
:
4%2Api%2Ar%5E2 = 40*pi
Divide both sides by 4pi
r^2 = 10
r = sqrt%2810%29
Find the Volume
V = %284%2F3%29%2Api%2A%28sqrt%2810%29%29%5E3
V = 132.46 cu/cm
:
:
And given that the area of an equilateral triangle is 67 cm^2, find its perimeter.
;
Let x = the side of the triangle;
Find the height:
h = sqrt%28x%5E2+-+%28.5x%29%5E2%29
h = sqrt%28.75x%5E2%29
Find x using the area:
%281%2F2%29%2Ax%2Asqrt%28.75x%5E2%29 = 67
Multiply both sides by 2
x%2Asqrt%28.75x%5E2%29 = 134
x%2Ax%2Asqrt%28.75%29 = 134
x%5E2%2Asqrt%28.75%29 = 134
x%5E2 = 134%2F%28sqrt%28.75%29%29
x^2 = 154.73
x = sqrt%28154.73%29
x = 12.44
:
P = 3(12.44)
P = 37.3 cm