Question

Each CD is approximately 4.72 inches in circumference and 0.05 inches in depth. There

are 15 CDs in the stack. Use the Cavalieri's Principle to find the surface area of the stack
of CDs. Justify your answer.
Answer
Blank 1

Answer 1

`SA=7.08\ in^2`

Explanation:

we know that

The Cavalieri's principle states that if two solids are of equal height and the sections "matching" equal areas everywhere along the height, the solids have the same volume.

The surface area of the stack is given by the formula

`SA=2B+LA`

where

B is the area of the base

LA is the lateral area

The lateral area of the stack, using Cavalieri's Principle, is equal to the lateral area of one CD multiplied by the total number of CDs of the stack

so

`LA=(4.72)(0.05)(15)=3.54\ in^2`

Find the radius of CD

Remember that the circumference is given by the formula

`C=2\pi r`

we have

`C=4.72\ in\\\pi=3.14`

substitute

`4.72=2(3.14) r`

solve for r

`r=0.75\ in`

Find the area of CD

`A=\pi r^(2)`

substitute

`A=(3.14)(0.75)^(2)=1.77\ in^2`

therefore

The surface area of the stack is equal to

`SA=2(1.77)+3.54=7.08\ in^2`