Question Video: Calculating the Radius of a Sphere given Its Surface Area | Nagwa Question Video: Calculating the Radius of a Sphere given Its Surface Area | Nagwa

Question Video: Calculating the Radius of a Sphere given Its Surface Area Mathematics • Second Year of Preparatory School

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Find the radius of the sphere whose surface area is 50 cm². Round your answer to two decimal places.

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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.

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