The area of a sphere is 196 sq. cm. Find the radius and volume of the sphere. Please show the solution.?

Question

please show your solution. it will serve as my lesson. i need to study it..

Answer 1

If by area you mean "Surface area" then

SA(sphere) = 4(pi)(r)^2

and

V(sphere) = 4(pi)(r)^3/3



Since SA = 196 cm^2, then



196cm^n = 4(pi)r^2

r^2 = 49/pi

r = 7/sqrt(pi) or approx. 3.949 cm



for the volume,

V = 4(pi)(r)^3/3

V = 4(pi)(7/pi^0.5)^3/3

V = (4pi/3)(343/pi^1.5)

V = (1372/(3pi^.5)) or approx. 258.02 cm^3



^_^ Hope this helps ^_^

Answer 2

Surface area of sphere = 196 cm^2 = 4(pi)r^2

r^2 = 196/(4pi)

r = sqrt(196/(4pi))

r = (approx.) 3.95 cm



Volume of sphere = (4/3)(pi)r^3

V = (4/3)(pi)(3.95^3)

V = (approx.) 258.023 cm^3

Answer 3

Area for sphere is 4*pi*r^2, so solve equation for r:



196=4*pi*r^2

49=pi*r^2

49/pi=r^2

7/sqrt(pi)=r



Then plug this value of r into the formula for volume,

V=4/3*pi*r^3

V=4/3*pi*(7/sqrt(pi))^3

V=1372/(3*sqrt(pi))=258.02