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
$V=\frac{\pi r^2h}{3}$

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:
$2616=\frac{3.14\times 10^2 \times h}{3}$

Simplifying the right hand side, we have
$2616=\frac{3.14 \times 100 \times h}{3} \\ \\2616=\frac{314h}{3}$

Multiply both sides by 3:
$2616\times 3=\frac{314h}{3}\times 3 \\ \\7848=314h$

Divide both sides by 314:
$\frac{7848}{314}=\frac{314h}{314} \\ \\24.99=h \\ \\25\approx h$

Answer 2

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

Step-by-step 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":

$Volume=\dfrac{1}{3}\times \pi\times r^2\times h\\\\2616=\dfrac{1}{3}\times 3.14\times 10\times 10\times h\\\\2616\times 3=314\times h\\\\7848=314\times h\\\\h=\dfrac{7848}{314}\\\\h=24.99\\\\h\approx 25\ cm$

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