Question

Two right circular cone x and y are made x having three times the radius of y and y having half the volume of x calculate the ratio between the height of x and y.

Answer 1

Complete math result .

Answer 2

Ratio between the height of x and y would be 2:9

Step-by-step explanation:

Since, the volume of a cone is,

$V=\frac{1}{3}\pi r^2 h$

Where,

r = radius,

h = height,

Let cone x has radius $r_1$ and height $h_1$,

Then its volume,

$V_1=\frac{1}{3}\pi r_1^2 h_1$

While let cone y has radius $r_2$ and height $h_2$,

The its volume,

$V_2=\frac{1}{3}\pi r_2^2 h_2$

$\implies \frac{V_1}{V_2}=\frac{r_1^2 h_1}{r_2^2 h_2}$

We have,

$r_1=3r_2, V_2=\frac{1}{2}V_1$

$\frac{V_1}{\frac{1}{2}V_1}=\frac{9r_2^2 h_1}{r_2^2 h_2}$

$\implies 2=\frac{9 h_1}{h_2}$

$\implies \frac{h_1}{h_2}=\frac{2}{9}$

Hence, ratio between the height of x and y would be 2:9.

#Learn more:

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