Question

A statue to honor Benjamin Franklin will be placed outside the entrance to the Liberty Bell exhibit hall in Philadelphia. The designers decide that a smaller, similar version will be placed on a table inside the building. The dimensions of the life-sized 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 weigh14 pounds.A. How much paint will be needed to paint the life-sized statue?B. If the small statue is made of the same material as the enlarged statue, then its weight will change just as the volume changes as the statue is enlarged. How much will the life-size statue weigh?

Answer 1

Given

The dimensions of the life-sized statue will be four times those of the smaller statue.

The painters need to paint 1.5 pints of paint to coat the small statue.

The weight of the small statue is 14 pounds.

To find:

a) How much paint will be needed to paint the life-sized statue?

b) If the small statue is made of the same material as the enlarged statue, then its weight will change just as the volume changes as the statue is enlarged. How much will the life-size statue weigh?

Step-by-step explanation:

a)

It is given that, the dimensions of the life sized statue is four times the dimension of the smaller statue.

Then, the scale factor is 4.

That implies, the surface area ratio is,

`\begin{gathered} Surface\text{ }Area=4^2 \\ =16 \end{gathered}`

Hence, the paint needed is,

`\begin{gathered} Required\text{ }paint=16*1.5 \\ =24pints \end{gathered}`

Hence, the paint needed to paint the life-sized statue is 24pints.

b)

The scale factor is 4.

Then,

`\begin{gathered} Volume\text{ }ratio=4^3 \\ =64 \end{gathered}`

That implies,

`\begin{gathered} Weight\text{ }of\text{ }Life-sized\text{ }statue=64*14 \\ =896pounds. \end{gathered}`

Hence, the weight of the life-size statue is 896 pounds.

Final result:

a) The paint needed to paint the life-sized statue is 24 pints.

b) The weight of the life-size statue is 896 pounds.