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Mathematics

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

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Answer

Given,

The surface area of the sphere = 154 cm2

∴4πr2=154⇒r2=1544π⇒r2=1544×227⇒r2=154×74×22⇒r2=494⇒r=494⇒r=72=3.5 cm\therefore 4πr^2 = 154 \\[1em] \Rightarrow r^2 = \dfrac{154}{4π} \\[1em] \Rightarrow r^2 = \dfrac{154}{4 \times \dfrac{22}{7}} \\[1em] \Rightarrow r^2 = \dfrac{154 \times 7}{4 \times 22} \\[1em] \Rightarrow r^2 = \dfrac{49}{4} \\[1em] \Rightarrow r = \sqrt{\dfrac{49}{4}} \\[1em] \Rightarrow r = \dfrac{7}{2} = 3.5 \text{ cm}

Hence, the radius of the sphere = 3.5 cm.

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