Question

Two similar wax statues have dimensions which are in the ratio 3:2,the volume of the smaller statu is 320cm^3 what is the volume of larger
statue if both have similar shapes

Answer 1

Given:

Two similar wax statues have dimensions which are in the ratio 3:2 , the volume of the smaller statue is 320 cm³.

To Find:

What is the volume of larger  statue? if both have similar shapes.

Solution:

If two figure or object are similar in shape, then:

Their ratio of area is equal to square of ratio of their respective side:

Also their ratio of volume is equal to cube of ratio of their respective side:

Means:

$\mathbf{\dfrac{V_{L}}{V_{s}}=\left ( \dfrac{X_{L}}{X_{s}} \right )^{3}}$

$\mathbf{V_{L}=Volume\ of\ larger\ statue= Unknown}$

$\mathbf{V_{s}=Volume\ of\ smaller\ statue= 320 \ cm^{3}}$

$\mathbf{Ratio\ of\ side\ of\ larger\ statue\ to\ smaller\ statue= \dfrac{X_{L}}{X_{s}}}=\dfrac{3}{2}}$

$\mathbf{\dfrac{V_{L}}{V_{s}}=\left ( \dfrac{X_{L}}{X_{s}} \right )^{3}}$

$\mathbf{\dfrac{V_{L}}{320}=\left ( \dfrac{3}{2} \right )^{3}}$

$\mathbf{\dfrac{V_{L}}{320}=\dfrac{9}{8}}$

On simplify:

$\mathbf{V_{L}=360 \ cm^{3}}$

Means volume of larger statue is 360 cm³

Answer 2

Answer:

1080cm^3........ volume= side ^3