Find the volume of a sphere whose surface area is 154 cm².

Let the radius of the sphere be r cm. Surface area = 154 cm²

rightwards double arrow

rightwards double arrow space space space space space space space space space space space space space space space space space space space space 4 πr squared equals 154 rightwards double arrow space space space space space space space space space space space space space space space 4 cross times 22 over 7 cross times straight r squared equals 154 rightwards double arrow space space space space space space space space space space space space space space space straight r squared equals fraction numerator 154 cross times 7 over denominator 4 cross times 22 end fraction rightwards double arrow space space space space space space space space space space space space space space space straight r squared equals 49 over 4 space space space space space space space space rightwards double arrow space straight r equals square root of 49 over 4 end root rightwards double arrow space space space space space space space space space space space space space space straight r equals 7 over 2 space cm

therefore

Volume of the sphere =

4 over 3 πr cubed

equals 4 over 3 cross times 22 over 7 cross times open parentheses 7 over 2 close parentheses cubed equals space 539 over 3 space cm cubed equals 179 2 over 3 space cm squared

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Find the volume of a sphere whose surface area is 154 cm2.

Surface Areas and Volumes

Mathematics

Find the volume of a sphere whose surface area is 154 cm².