Respuesta :
The correct answer is:
25 cm.
Explanation:
The volume of a cone is given by the formula
[tex]V=\frac{\pi r^2h}{3}[/tex]
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:
[tex]2616=\frac{3.14\times 10^2 \times h}{3}[/tex]
Simplifying the right hand side, we have
[tex]2616=\frac{3.14 \times 100 \times h}{3} \\ \\2616=\frac{314h}{3}[/tex]
Multiply both sides by 3:
[tex]2616\times 3=\frac{314h}{3}\times 3 \\ \\7848=314h[/tex]
Divide both sides by 314:
[tex]\frac{7848}{314}=\frac{314h}{314} \\ \\24.99=h \\ \\25\approx h[/tex]
25 cm.
Explanation:
The volume of a cone is given by the formula
[tex]V=\frac{\pi r^2h}{3}[/tex]
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:
[tex]2616=\frac{3.14\times 10^2 \times h}{3}[/tex]
Simplifying the right hand side, we have
[tex]2616=\frac{3.14 \times 100 \times h}{3} \\ \\2616=\frac{314h}{3}[/tex]
Multiply both sides by 3:
[tex]2616\times 3=\frac{314h}{3}\times 3 \\ \\7848=314h[/tex]
Divide both sides by 314:
[tex]\frac{7848}{314}=\frac{314h}{314} \\ \\24.99=h \\ \\25\approx h[/tex]
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":
[tex]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[/tex]
Hence, Distance should be 25 cm from the source to the detector.
