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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. - Mathematics

Answer in Brief

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.

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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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APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Q 32 | Page 82
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