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Question
The surface area of a sphere is the same as the curved surface area of a cone having the radius of the base as 120 cm and height 160 cm. Find the radius of the sphere.
Solution
Lateral height of cone
`l = sqrt((120)^2 +(160)^2)`
`= sqrt(14400 + 25600)`
`= sqrt 40000`
`= sqrt 200`
Surface area of sphere = surface area of cone
\[4 \pi r_1^2 = \pi r l\]
\[ {r_1}^2 = \frac{rl}{4}\]
\[ {r_1}^2 = \frac{120 \times 200}{4}\]
\[ {r_1}^2 = 6000\]
Radius of sphere
`r_1 = sqrt6000`
`= 77.46 cm`
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