Question

if the volumes of two cones are in the ratio 4:5 and their radi are in ratio 2:3 what is the ratio of their heights​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The ratio of their heights​ is $\mathbf{\frac{9}{5} }$

Step-by-step explanation:

• Given data

        Ratio of volume of two cone is 4:5

        Means

        $\mathbf{\frac{V_{1}}{V_{2}}=\frac{4}{5}}$             ...1)

• Ratio of radius of cone is 2:3

        $\mathbf{\frac{R_{1}}{R_{2}}=\frac{2}{3}}$

• We can also write the relation between volume ,radius and height of cone

        $\mathbf{\frac{V_{1}}{V_{2}}=\frac{\frac{1}{3}\pi R_{1}^{2}H_{1}}{\frac{1}{3}\pi R_{2}^{2}H_{2}}}$

        So

        $\mathbf{\frac{V_{1}}{V_{2}}=\left ( \frac{R_{1}}{R_{2}} \right )^{2}\times \frac{H_{1}}{H_{2}}}$

• On putting respective value in above equation

         $\mathbf{\frac{4}{5}=\left ( \frac{2}{3} \right )^{2}\times \frac{H_{1}}{H_{2}}}$

        On solving

         $\mathbf{\frac{H_{1}}{H_{2}}=\frac{9}{5} }$   This is the ratio of their heights