Mark has made a clay model.

He will now make a clay statue that is mathematically similar to the clay model.

The model has a base area if 6cm^2.
The statue will have a base area of 253.5cm^2.

Mark used 2kg of clay to make the model.

Clay is sold in 10kg bags.
Mark has to but all the clay he needs to make the statue.

How many bags of clay will Mark need to buy?

Thank you.

2 answers

The two areas of similar objects are proportional to the square of their corresponding sides.
The two volumes of similar objects are proportional to the cubes of their corresponding sides.

sides of model^2 : sides of statue^2 = 6 : 253.5
side of model : side of statue = √6 : √253.5

Let's assume that the volume is proportional to the mass, let the mass of the statue be M

2 : M = (√6)^3 : (√253.5)^3
2(√6)^3 M = (√253.5)^3
M = (√253.5)^3 / 2(√6)^3
= 274.625 kg

So he needs 274.625/10 bags of clay
= 27.46 bags

So he must buy 28 bags of clay
He will need

(253.5/6)^(3/2) * 2 = 549.25 kg of clay

So, he will need 55 10kg bags