Question

B) The number of volume of a cylinder is half of its number of the total surface area.

If the radius of its base is 7 cm, find the volume.​

Answer 1

`V=179.6cm^3`

Explanation:

the volume of a cylinder is given by:

`V=\pi r^2h`

where r is the radius and h is the height.

and the surface area:

`SA=2\pi r^2+2\pi rh`

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:

`V=(1)/(2)SA`

substitutig the equivalent expressions on each side:

`\pi r^2 h = (1)/(2) (2\pi r^2+2\pi r h)`

and we simplify and solve for the height (since is the value we don't know of the cylinder):

`\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)`

we substitute the value of the radius
`r=7cm`, and we get:

`h=\pi (7cm)^2/(\pi (7cm)^2-\pi (7cm))\\h=153.938/(153.938-21.991)\\h=153.938/131.947\\h=1.1666cm`

thus the volume is:

`V=\pi r^2h`

`V=\pi (7cm)^2(1.1666cm)\\V=179.6cm^3`