Question

If a sphere has the same curved surface area as total surface area of cone of vertical height $40cm$ and radius $30cm$ then the radius of the sphere is:

• A. $10\sqrt{6}$ cm
• B. $10\sqrt{3}$ cm
• C. $10\sqrt{2}$ cm
• D. $12cm$

Answer 1

The correct option is B $10\sqrt{3}$ cm

Given the vertical height of cone is 40 cm and radius is 30 cm

Then surface area of cone=$\pi rh=\pi \times 30\times 40=1200\pi c{m}^2$

The surface area of cone =coveredsurface area of sphere

$\therefore \pi R^2=1200\pi \Rightarrow R^2=300\Rightarrow R=10\sqrt{3}cm$

Then the radius of sphere =$10\sqrt{3}cm$