Respuesta :
Answer:
[tex]V=179.6cm^3[/tex]
Step-by-step explanation:
the volume of a cylinder is given by:
[tex]V=\pi r^2h[/tex]
where r is the radius and h is the height.
and the surface area:
[tex]SA=2\pi r^2+2\pi rh[/tex]
the first term is the area of the circles and the second term is the area of the body.
since "The number of volume of a cylinder is half of its number of the total surface area." we will have that:
[tex]V=\frac{1}{2}SA[/tex]
substitutig the equivalent expressions on each side:
[tex]\pi r^2 h = \frac{1}{2} (2\pi r^2+2\pi r h)[/tex]
and we simplify and solve for the height (since is the value we don't know of the cylinder):
[tex]\pi r^2 h = \pi r^2+\pi r h\\\pi r^2h-\pi rh=\pi r^2\\h(\pi r^2-\pi r)=\pi r^2\\h=\pi r^2/(\pi r^2-\pi r)[/tex]
we substitute the value of the radius [tex]r=7cm[/tex], and we get:
[tex]h=\pi (7cm)^2/(\pi (7cm)^2-\pi (7cm))\\h=153.938/(153.938-21.991)\\h=153.938/131.947\\h=1.1666cm[/tex]
thus the volume is:
[tex]V=\pi r^2h[/tex]
[tex]V=\pi (7cm)^2(1.1666cm)\\V=179.6cm^3[/tex]
