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a statue on honor Benjamin Franklin will be placed outside the entrance to the Liberty Bell Exhibit Hall in Philadelphia the designers that is the side that is smaller similar version will be placed on a table inside the building the dimensions of the life-size statue will be four times those of the smaller statue. planners expect to need 1.5 pints of paint to coat the small statue they also know that the small statue will weight 14 pounds. how much paint will be needed to paint the life sized statue ​

Respuesta :

calculista

Answer:

Part a) The paint needed will be [tex]24\ pints[/tex]

Part b) The weight of the life sized statue  is [tex]896\ lb[/tex]

Step-by-step explanation:

step 1

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z----> the scale factor

x----> surface area of the life sized statue

y----> surface area of the smaller statue

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=4[/tex]

substitute

[tex]4^{2}=\frac{x}{y}[/tex]

[tex]x=16y[/tex]

The surface area of the life sized statue  is 16 times the surface area of the smaller statue

therefore

The paint needed will be

[tex]16(1.5)=24\ pints[/tex]

step 2

Find the weight of the life sized statue

we know that

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

Let

z----> the scale factor

x----> weight of the life sized statue

y----> weight of the smaller statue

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

we have

[tex]z=4[/tex]

[tex]y=14\ lb[/tex]

substitute

[tex]4^{3}=\frac{x}{14}[/tex]

[tex]x=64(14)=896\ lb[/tex]