Question

A sphere has a surface area of 200 square centimeters. Which choice is the best approximation of its diameter? Use 3.14 to approximate pi.

Answer 1

SA = surface area of the sphere
SA = 4*pi*r^2
200 = 4*pi*r^2
200 = 4*3.14*r^2
200 = 12.56*r^2
12.56*r^2 = 200
r^2 = 200/12.56
r^2 = 15.9235668789809
r = sqrt(15.9235668789809)
r = 3.99043442233811

The radius is r = 3.99043442233811
so the diameter is
d = 2*r
d = 2*3.99043442233811
d = 7.98086884467621

Answer: 7.98086884467621
Round this however you need to

Answer 2

11.29 cm is the diameter.

Explanation:

A sphere is given with a surface area of 200 square cm.

We have to calculate the diameter of this sphere.

Surface area of sphere = 4πr² = 4×3.14×r² = 400

r² = 400/(4×3.14) = 100/3.14

r = √(100/3.14) = 10/√3.14 = 10/1.772 = 5.64 cm.

Therefore diameter = 2×r = 2×5.64 = 11.29 cm. is the answer.