Question

The digital volume of a cone beam x-ray scan is 2616 cm³. To capture a craniofacial image on the detector, the base of the cone beam on the detector must have a diameter of 20 cm. What should the distance be from the source to the detector (i.e., the height of the cone beam)? Use π=3.14 and round your answer to the nearest whole number.

Answer 1

The correct answer is:

25 cm.

Explanation:

The volume of a cone is given by the formula

`V=(\pi r^2h)/(3)`

The diameter is 20 cm, so the radius is half of that:
20/2=10 cm.

Our volume is 2616 and we will use 3.14 for pi:

`2616=(3.14* 10^2 * h)/(3)`

Simplifying the right hand side, we have

`2616=(3.14 * 100 * h)/(3) \\ \\2616=(314h)/(3)`

Multiply both sides by 3:

`2616* 3=(314h)/(3)* 3 \\ \\7848=314h`

Divide both sides by 314:

`(7848)/(314)=(314h)/(314) \\ \\24.99=h \\ \\25\approx h`

Answer 2

Answer: Distance should be 25 cm from the source to the detector.

Explanation:

Since we have given that

Volume of cone beam x-ray scan = 2616 cm³

Diameter of cone beam = 20 cm

Radius of cone beam = 10 cm

Le the height of the cone beam be 'h'.

As we know the formula for "Volume of cone":

`Volume=(1)/(3)* \pi* r^2* h\\\\2616=(1)/(3)* 3.14* 10* 10* h\\\\2616* 3=314* h\\\\7848=314* h\\\\h=(7848)/(314)\\\\h=24.99\\\\h\approx 25\ cm`

Hence, Distance should be 25 cm from the source to the detector.