SOLUTION: Sphere A has a diameter that is twice the diameter of sphere B. If 9 gallons of paint are needed to cover the outside of sphere A, how much paint is needed to cover the outside of
Algebra.Com
Question 752644: Sphere A has a diameter that is twice the diameter of sphere B. If 9 gallons of paint are needed to cover the outside of sphere A, how much paint is needed to cover the outside of sphere B?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
surface area of a sphere is equal to 4 * pi * r^2
sphere A has a diameter that is 2 times the diameter of sphere B.
this means that sphere A has a radius that is 2 times the radius of sphere B.
if we let the radius of sphere B equal to x, then the radius of sphere A is equal to 2x.
the surface area of sphere A is equal to 4 * pi * (2x)^2 which is equal to 4 * pi * 4x^2 which is equal to 16 * pi * x^2
the surface area of sphere B is equal to 4 * pi * x^2 which is equal to 4 * pi * x^2.
the surface area of sphere A divided by the surface area of sphere B is equal to 16 * pi * x^2 / (4 * pi * x^2 which means that the surface area of sphere A is 4 times the surface area of sphere B.
if it took 9 gallons to cover sphere B, then it will take 36 gallons to cover sphere A.
RELATED QUESTIONS
A sphere with the diameter 5 feet is being painted. How much more paint would be needed... (answered by josgarithmetic,ikleyn)
The mass of a sphere is proportional to its radius cubed. If a sphere of diameter 2 cm... (answered by drk)
If 1 gallon of paint covers 400 square feet, about howmany gallons of paint are needed to (answered by Marth)
if a sphere has a diameter of 30 what is half the volume of the... (answered by Alan3354)
a sphere has a diameter of 4 cm. what is the volume of the... (answered by edjones)
A painter needs to paint a circular floor that is 24 yards in diameter. A gallon of paint (answered by ankor@dixie-net.com)
If a sphere has a diameter of 22 units, then what is the surface area of the sphere (answered by Alan3354)
Find the volume of a sphere that has a diameter of 9 meters. (answered by nerdybill)
Find the volume of a sphere that has a diameter of 9... (answered by checkley77,uday1435)