Question

3. The Surface area of Sphere of radius
5cm is 5 times the C.S.A of
cone 4 cm find the height and volume
of the Cone.
​

Answer 1

Solution-

Radius of sphere => 5cm

Radius of cone => 4cm

Surface area of sphere = 5 * ( curved surface area of cone )

$4\pi \: {r}^{2} = > 5 \times \pi \: rl \\ \\ l = > \frac{4\pi \: {r}^{2} }{5\pi \: r} \\ \\ l = > r \: of \: sphere\\ \\ \boxed{ l = > 5cm}$

$height \: of \: cone = \sqrt{ {l}^{2} - {r}^{2} } \\ \\ = > \sqrt{ {5}^{2} - {4}^{2} } \\ \\ = > \sqrt{25 - 16} \\ \\ = > \sqrt{9} \\ \\ = > 3cm$

$volume \: of \: cone \: = > \frac{\pi \: {r}^{2}h }{3} \\ \\ = > \frac{22 \times 4 \times 4 \times 3}{7 \times 3} \\ \\ = > \frac{352}{7} c {m}^{3} \\ \\ = > 50.28c {m}^{3}$

The height of cone => 3cm

The volume of cone => 50.28cm³

Hope it's helpful you