The surface area of a sphere is the same as the

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

$l=\sqrt{(120)^{2}+(160)^{2}}$

$=\sqrt{14400+25600}$

$=\sqrt{40000}$

 

$=200$

Surface area of sphere = surface area of cone

$4 \pi \mathrm{r}_{1}{ }^{2}=\pi \mathrm{rl}$

$\mathrm{r}_{1}{ }^{2}=\frac{r l}{4}$

$\mathrm{r}_{1}^{2}=\frac{120 \times 200}{4}$

$\mathrm{r}_{1}^{2}=6000$

Radius of sphere

$r_{1}=\sqrt{6000}$

$=77.46 \mathrm{~cm}$

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