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Bryan is an art sculptor and is creating an art series made entirely of similar figures. He buys a Sponge Bob Square Pants figure and decides he wants to make a larger version that has sides 15 times bigger. If the area of the figure is 12.5 cm2, what is the area of his sculpture?

Bryan is an art sculptor and is creating an art series made entirely of similar figures He buys a Sponge Bob Square Pants figure and decides he wants to make a class=

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Answer:

The area of sculpture is 2812.5 cm².

Step-by-step explanation:

If two figures are similar then the ratio of their areas are equal to the ratio of square of corresponding sides.

The area of figure is 12.5  cm² and the sides of sculpture is 15 times of the figure.

Let the area of sculpture be x.

[tex]\frac{\text{Area of sculpture}}{\text{Area of figure}}=\frac{(15)^2}{1^2}[/tex]

[tex]\frac{x}{12.5}=225[/tex]

Multiply both sides by 12.5.

[tex]x=225\times 12.5[/tex]

[tex]x=2,812.5[/tex]

Therefore the area of sculpture is 2812.5 cm².

Answer:

The area of Bryan's sculpture is 2812.5 cm^2.      

Step-by-step explanation:

S1. Identify the information given.

Of larger sculpture: A = ?      

Of smaller  figure: A' = 12.5  cm^2        

Ratio of the sides: s/s' =  15/1.      

S2.  Find the ratio of the areas.

   A/A' = (s/s')^2  = (15/1)^2  =      225/1

S3. Substitute known area into proportion.

A/12.5 = 225/1

S4. Cross multiply, solve for A              .

A(1) = 12.5(225)

A =    2812.5

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