Question

The height of a cone is $60cm$. A small cone is cut off at the top by a plane parallel to the base and its volume is ${\frac{1}{64}}^{th}$ the volume of original cone. The height from the base at which the section is made is:

• A. $30cm$
• B. $15cm$
• C. $45cm$
• D. $20cm$

Answer 1

Answer: (B)

Now, $V_{CuttedCone}=\frac{1}{64}{V}_{Original}\frac{1}{3}\pi x^{2}l=\frac{1}{64}\times \frac{1}{3}\pi R^{2}60$

$\Rightarrow (\frac{x}{R}{)}^{2}l=\frac{60}{64}$

According to properties of similar triangles

$\frac{l}{x}=\frac{60}{R}\Rightarrow \frac{x}{R}=\frac{l}{60}$

$\Rightarrow (\frac{l}{60}{)}^{2}l=\frac{60}{64}\Rightarrow l^3=\frac{3600\times 60}{64}\Rightarrow l=\frac{60}{4}=15$

Therefore, the answer is $15cm$