SOLUTION: The formula for the surface area of a sphere is {{{A=4*pi*r^2}}}, where A is surface area and r is the radius of the sphere a) use the formula {{{A=4*pi*r^2}}} to express

SOLUTION: The formula for the surface area of a sphere is {{{A=4pir^2}}}, where A is surface area and r is the radius of the sphere a) use the formula {{{A=4pir^2}}} to express

Question 83801: The formula for the surface area of a sphere is
, where A is surface area and r is the
radius of the sphere

a) use the formula to express r in terms of A and
rationalize the denominator. Explain your answer

b) suppose the surface area of a child's ball is
about 113 square inches. Find the radius of the
ball and explain your steps.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The formula for the surface area of a sphere is
, where A is surface area and r is the
radius of the sphere

a) use the formula to express r in terms of A and
rationalize the denominator. Explain your answer
Since we can solve for r by these steps

Start with the given equation

Divide both sides by

Take the square root of both sides

Break up the square root using the identity }

Break up the square root using the identity }

Take the square root of 4 to get 2

Now rationalize the denominator by multiplying the numerator and denominator by . This is equivalent to which in other words eliminates the square root in the denominator

Multiply and reduce

Combine the square roots in the numerator

So now we have an equation in terms of A which is

b) suppose the surface area of a child's ball is
about 113 square inches. Find the radius of the
ball and explain your steps.

Since we have an equation in terms of A, we can plug in the given surface area (113 sq in) in for A and solve for r

Plug in A=113

Now lets approximate to 3.14. From here on, all of our values will be approximations. So even though I don't show it (I'm unable to), keep this in mind.

Replace with 3.14

Multiply

Take the square root

Divide

So the for a ball with a surface area of 113 sq in., the radius is about 3 inches
RELATED QUESTIONS
The formula for the surface area of a sphere is pi r^2, where A is surface area and r is... (answered by ccs2011)

Find the radius of a sphere with surface area 160in squared. use the formula... (answered by Earlsdon)

The radius r of a sphere in terms of its surface area A is given by the formula... (answered by It is costly)

The surface area (A) of a sphere with the radius (r) is given by A = 4(3.14)r^2. Solve... (answered by Alan3354)

The surface area (A) of a sphere with radius (r) is given by A=4πr^2. Solve this... (answered by Alan3354)

Find the volume in terms of pi of a sphere whose surface area is {{{36*pi^2}}}. The... (answered by bucky)

The problem reads: The surface area of a sphere is given by S=4(pi)r^2, where r is the (answered by solver91311)

state the formula for the surface area S of a sphere of radius... (answered by Fombitz)

Sphere B has 4 times the surface area of sphere A. How many times the volume of sphere A... (answered by richwmiller,amoresroy)