SOLUTION: There are 3 spherical balls. The radius of the middle sized ball is twice the radius of the small ball. The radius of the largest ball is 5cm larger than the radius of the smallest
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Question 810880: There are 3 spherical balls. The radius of the middle sized ball is twice the radius of the small ball. The radius of the largest ball is 5cm larger than the radius of the smallest ball. The surface area of the largest ball is equal to the sum of the surface areas of the two smaller balls. Find the radius of the middle sized ball. Note: the surface area of a sphere given is by the formula SA =4πr^2
I cant seem to get the correct answer which is around 8.02 and 8.09
Ive tried to form equations for them and they're below
The equation for radius
Medium ball : 2r
Large ball : r+5
Small ball : r
Equations for surface area
middle ball : a
Large ball : a+b
small ball: b
I dont know where to go from here, please help
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
radius
small ball x
middle ball 2x
large ball x+5
surface area of large ball = 4*pi*(x+5)^2
middle ball ---4*pi*(2x)2
small ball -------4*pi*x^2
sum= 16pix^2+4pix^2= 20 pix^2
20pix^2=4pi(x+5)^2
5x^2=(x+5)^2
5x^2=x^2+10x+25
4x^2-10x-25=0
Find the roots of the equation by quadratic formula
iiiii
a= 4 , b= -10 , c= -25
b^2-4ac= 100 + 400
b^2-4ac= 500
x1=( 10 + 22.36 )/ 8
x1= 4.05
x2=( 10 -22.36 ) / 8
x2= -1.55
ignore negative
x= 4.05_________ small ball
2x= 8.1___________middle ball
x+5=9.05___________large ball
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