Answer:
B) Yolanda should have found the volume by multiplying 8 by 4/3.
Step-by-step explanation:
The height of a sphere is equal to its diameter, which is twice its radius. Therefore, if a sphere and a cylinder have the same radius and height, the height of the cylinder is 2r.
The formula for the volume of a cylinder is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Cylinder}}\\\\V=\pi r^2 h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius of the circular base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]
Given that the volume of the cylinder is 8 m³, we can substitute V = 8 and h = 2r into the volume of a cylinder formula to give:
[tex]\pi r^2 \cdot r = 8\\\\\pi r^3 = 8[/tex]
The formula for the volume of a sphere is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Sphere}}\\\\V=\dfrac{4}{3}\pi r^3\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius.}\end{array}}[/tex]
Given that the sphere has the same radius as the cylinder, and we know that πr³ = 8, we can substitute this into the volume of a sphere equation:
[tex]V=\dfrac{4}{3} \cdot 8[/tex]
Therefore, Yolanda's error is that she should have found the volume by multiplying 8 by 4/3, not by multiplying the cube of 8 by 4/3.
[tex]\dotfill[/tex]
Yolanda's work:
V = 4/3 (8)^3
V = 4/3 (512)
V = 2048/3 m^3