Respuesta :
The volume of the sphere is [tex]V(sphere) = \frac{2}{3}(27\pi )[/tex]
What is volume of the sphere ?
"The volume of sphere is the amount of space occupied, within the sphere. The sphere is defined as the three-dimensional round solid figure in which every point on its surface is equidistant from its center. The fixed distance is called the radius of the sphere and the fixed point is called the center of the sphere."
What is volume of the cylinder ?
"A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up. Thus, the volume of the cylinder can be given by the product of the area of base and height."
We have
Volume of cylinder = 27[tex]\pi[/tex] feet cubed
According to the question,
A sphere and a cylinder have the same radius (r) and height (h).
Formula for volume of cylinder
[tex]V(cylinder) = \pi r^{2}h[/tex]
⇒[tex]27\pi = \pi r^{2}h[/tex]
⇒[tex]r^{2} h = 27[/tex]
Formula for volume of sphere
[tex]V(sphere) = \frac{4}{3} \pi r^{3}[/tex]
⇒ [tex]V(sphere) = \frac{2}{3}.(2) \pi (r^{2}.r)[/tex]
⇒ [tex]V(sphere) = \frac{2}{3}. \pi r^{2}.(2r)[/tex]
Height of the sphere (h) = 2r
[tex]V(sphere) = \frac{2}{3}. \pi r^{2}h[/tex]
Substitute [tex]r^{2} h = 27[/tex] in equation of volume of sphere
[tex]V(sphere) = \frac{2}{3}. \pi (27)[/tex]
⇒ [tex]V(sphere) = \frac{2}{3}(27\pi )[/tex]
The volume of the sphere is [tex]V(sphere) = \frac{2}{3}(27\pi )[/tex]
Hence, volume of the sphere V = two-thirds (27pi)
Learn more about volume of the sphere and volume of the cylinder here
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Answer:
A
Step-by-step explanation:
The person above is correct
