Question

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?

Answer 1

The weight of the enlarged paperweight is
`1.2\ lb`

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

`z^(3)=(x)/(y)`

we have

`z=2`

`y=0.15\ lb`

substitute and solve for x

`2^(3)=(x)/(0.15)`

`x=2^(3)(0.15)=1.2\ lb`