Question 191520
Given the surface area of a sphere is 40 pi cm^2, find its volume.
:
Two formulas: V = {{{(4/3)*pi*r^3}}} & SA = {{{4*pi*r^2}}}
:
{{{4*pi*r^2}}} = 40*pi
Divide both sides by 4pi
r^2 = 10
r = {{{sqrt(10)}}}
Find the Volume
V = {{{(4/3)*pi*(sqrt(10))^3}}}
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(x^2 - (.5x)^2)}}}
h = {{{sqrt(.75x^2)}}}
Find x using the area:
{{{(1/2)*x*sqrt(.75x^2)}}} = 67
Multiply both sides by 2
{{{x*sqrt(.75x^2)}}} = 134
{{{x*x*sqrt(.75)}}} = 134
{{{x^2*sqrt(.75)}}} = 134
{{{x^2}}} = {{{134/(sqrt(.75))}}}
x^2 = 154.73
x = {{{sqrt(154.73)}}}
x = 12.44
:
P = 3(12.44)
P = 37.3 cm