Question

Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is

• A. 8 cm
• B. \(4\sqrt{5}\) cm
• C. \(2\sqrt{5}\) cm
• D. 12 cm

Hint:

Use the Pythagoras theorem: \(l^2 = r^2 + h^2\) in right-angled triangles of cones.

Answer 1

The Correct Option is B

\[ \text{Using Pythagoras theorem: } l^2 = r^2 + h^2 \Rightarrow 6^2 = 4^2 + h^2 \Rightarrow 36 = 16 + h^2 \] \[ h^2 = 20 \Rightarrow h = \sqrt{20} = 2\sqrt{5} \] \[ \text{Since two identical cones are joined, total height} = 2 \times 2\sqrt{5} = 4\sqrt{5} \text{ cm} \]