Question

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?

Answer 1

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

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

Answer 2

The area of sculpture is 2812.5 cm².

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.

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

`(x)/(12.5)=225`

Multiply both sides by 12.5.

`x=225* 12.5`

`x=2,812.5`

Therefore the area of sculpture is 2812.5 cm².