contestada

A marble paperweight shaped similar to a cone weighs 0.15 lb. How much does a similarly shaped paperweight weigh if its radius and height are twice as large?

Respuesta :

Answer:

The weight of the enlarged paperweight is [tex]1.2\ lb[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes (or its weights) is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x ----> the enlarged paperweight weight

y ----> the original paperweight weight

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=2[/tex]

[tex]y=0.15\ lb[/tex]

substitute and solve for x

[tex]2^{3}=\frac{x}{0.15}[/tex]

[tex]x=2^{3}(0.15)=1.2\ lb[/tex]