Question

6. The volumes of two cones of same base radius are 3600 cm3 and 5040 cm3. Find the

ratio of heights.​

Answer 1

The volumes of two cones of same base radius are 3600 cm3 and 5040 cm3.
3:5

Answer 2

The ratio of heights is 5:7.

Step-by-step explanation:

It is given that the volumes of two cones of same base radius are 3600 cm³ and 5040 cm³.

The volume of a cone is

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

where, r is radius and h is height.

Let radius of first cone is r and height is h₁. Radius of second cone is r and height is h₂.

$V_1=\dfrac{1}{3}\pi r^2h_1$

$V_2=\dfrac{1}{3}\pi r^2h_2$

Ratio of volumes is

$\dfrac{V_1}{V_2}=\dfrac{3600}{5040}$

$\dfrac{\dfrac{1}{3}\pi r^2h_1}{\dfrac{1}{3}\pi r^2h_2}=\dfrac{3600}{5040}$

Cancel out common factors.

$\dfrac{h_1}{h_2}=\dfrac{5}{7}$

Therefore, the ratio of heights is 5:7.

#Learn more

The height of cone is 15 CM if its volume is 1530 cm3 find the radius of the base.

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