a sphere has a volume of 500/3 pi cubic centimeters. What is the total surface area, in sqaure cntimeters, of the square?
A. 25 pi
B. 40 pi
C. 100 pi
D. 400 pi
Please show your work. im very confused :(
Volume= 4/3 PI r^3
Area= 4PI r^2
(500/3)PI=4/3 PI r^3
r= cubrt(125)=5cm
so area is ....
To find the total surface area of a sphere, you can use the formula:
Surface Area = 4πr^2
Given that the volume of the sphere is 500/3π cubic centimeters, you can use the formula for the volume to find the radius (r).
Volume = (4/3)πr^3
500/3π = (4/3)πr^3
Simplifying both sides by canceling out π:
500/3 = 4/3r^3
Multiply both sides by 3/4:
(500/3) * (3/4) = r^3
500/4 = r^3
Taking the cube root of both sides, you get:
∛(500/4) = r
Now that you have the radius (r), you can substitute it into the formula for the surface area to find the total surface area (A).
Surface Area = 4πr^2
Surface Area = 4π * (∛(500/4))^2
Calculating the value inside the parentheses first:
∛(500/4) ≈ 4.5199
Then calculate the square of that value:
(4.5199)^2 ≈ 20.4417
Finally, substitute this value into the surface area formula:
Surface Area = 4π * 20.4417
Calculating the value inside the parentheses:
4π * 20.4417 ≈ 25.5717π
Therefore, the total surface area of the sphere is approximately 25.5717π square centimeters. Since none of the answer choices match this value exactly, I cannot provide a specific answer, but the closest option is A) 25π.