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olchik [2.2K]
3 years ago
10

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

Mathematics
1 answer:
Alecsey [184]3 years ago
5 0

Answer:

SA=7.08\ in^2

Step-by-step explanation:

we know that

The <u><em>Cavalieri's principle</em></u> 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

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