Question

Please help. how much would the statue weigh if the original was 10
feet?

Answer 1

Part a) The weight of the original statue is
`9,483\ pounds`

The ratio of the height of the original statue to the height of the small statue is 8.4

The ratio of the weights or volumes is
`8.4^(3)`

Part b)
`221,184\ pounds`

Explanation:

Part a)

we know that

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

step 1

Find the scale factor

remember that

`1\ ft=12\ in`

The original statue is 7 ft tall

Convert to inches

`7\ ft=7*12=84\ in`

Divide the height of the original statue by the height of the model to find the scale factor

`(84)/(10)=8.4`

step 2

Find the ratio of its weights

Let

z-----> the scale factor

x-----> the weight of the original statue

y----> the weight of the model

so

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

we have

`z=8.4`

`y=16\ lb`

substitute

`8.4^(3)=(x)/(16)`

`x=16(8.4^(3))=9,483\ pounds`

The weight of the original statue is
`9,483\ pounds`

The ratio of the height of the original statue to the height of the small statue is 8.4

The ratio of the weights or volumes is
`8.4^(3)`

Part b) If the original statue were 20 ft tall, how much would it weight?

step 1

Find the scale factor

remember that

`1\ ft=12\ in`

The original statue is 20 ft tall

Convert to inches

`20\ ft=20*12=240\ in`

Divide the height of the original statue by the height of the model to find the scale factor

`(240)/(10)=24`

step 2

Find the ratio of its weights

Let

z-----> the scale factor

x-----> the weight of the original statue

y----> the weight of the model

so

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

we have

`z=24`

`y=16\ lb`

substitute

`24^(3)=(x)/(16)`

`x=16(24^(3))=221,184\ pounds`