Video Transcript
Find the radius of the sphere whose
surface area is 50 square centimeters. Round your answer to two decimal
places.
We’ve been given the surface area
of a sphere and asked to determine its radius. To do this, we need to recall how
the surface area of a sphere is calculated. We use the formula four 𝜋𝑟
squared, where 𝑟 represents the radius of the sphere. We can use this knowledge and the
given surface area to form an equation.
The surface area is 50 square
centimeters, so we have the equation four 𝜋𝑟 squared equals 50. We now solve this equation for
𝑟. First, we divide each side of the
equation by four 𝜋, giving 𝑟 squared equals 50 over four 𝜋. This fraction can be simplified by
canceling a factor of two in the numerator and denominator to give 𝑟 squared equals
25 over two 𝜋.
Next, we take the square root of
both sides of the equation, taking only the positive value as 𝑟 represents a length
and so is, by definition, a positive value. We have 𝑟 equals the square root
of 25 over two 𝜋. Evaluating this on a calculator
gives 1.99471 continuing. We’re asked to give the answer to
two decimal places, so we round down. And we’ve found that the radius of
the sphere whose surface area is 50 square centimeters is 1.99 centimeters to two
decimal places.
