Question

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)^3
V=4/3(512)
V=2048/3 m ^3

What 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 4/3
Yolanda should have found the volume with the formula V=2/3(3.14)8 ^3
Yolanda should have found the volume with the formula V=2/3 8^3

Answer 1

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.

Answer 2

Answer:

The correct answer is 28m³