Question

Mr. Gatting poured the same amount of pepper into each of the cylindrical pepper shakers shown below. The pepper in the shaker on the left is
filled to a height of 45 millimeters.
60 mm
OA 60 millimeters
OB. 95 millimeters
-32 mm
To what approximate height is the shaker on the right filled with pepper?
24 mm-
Note: Figures are not drawn to scale
100 mm

Answer 1

Answer:

80 mm

Step-by-step explanation:

the same amount (and that means the same volume) of pepper is in each shaker.

the volume of a cylinder is

base area × height = pi×r² × height

with r being the radius (which is always half of the diameter).

the volume of the filled in pepper in the first shaker is then

pi×(32/2)²×45 = pi×16²×45 = pi×256×45 = 11,520pi mm³ =

= 36,191.14737... mm³

now let's see what height in the second shaker we will reach by filling the same 11,520pi mm³ of pepper into it.

so, we have

pi×(24/2)²×height = 11,520pi

12²×height = 11,520

144×height = 11,520

height = 11,520/144 = 80 mm

so, the shaker on the right is filled up to 80 mm with pepper.