A sphere and a cylinder have the same radius and height. The volume of the cylinder is 8 m^3. Yolanda found the volume of the sphere.(please see attached picture)Her work is shown below.V=4/3(8)^3V=4/3(512)V=2048/3 m ^3What is Yolanda’s error?Yolanda should have found the volume by multiplying 8 by 2/3.Yolanda should have found the volume by multiplying 8 by 4/3Yolanda should have found the volume with the formula V=2/3(3.14)8 ^3Yolanda should have found the volume with the formula V=2/3 8^3
Accepted Solution
A:
we know that the height of cylinder is equal to the diameter of sphere so h=2*r------> equation 1
volume of cylinder=pi*r²*h volume=8 m³ substitute equation 1 in the formula of volume 8=pi*r²*(2*r)------> 8=2*pi*r³-----> equation 2
find the volume of a sphere volume sphere=(4/3)*pi*r³-----> (2/3)*[2*pi*r³] substitute the equation 2 in the formula of volume volume sphere=(2/3)*[8]----> 16/3 m³
the answer is Yolanda should have found the volume by multiplying 8 by 2/3.