The formula for the volume of a cone is:
#V_c = pir^2h/3#
To find the radius we divide the diameter by #2# giving:
#(4"in")/2 = 2"in"#
Substituting #2"in"# for #r# and #6"in"# for #h# and calculating #V_c# gives:
#V_c = pi xx (2"in")^2 xx (6"in")/3#
#V_c = pi xx 4"in"^2 xx 2"in"#
#V_c = pi xx 8"in"^3#
Using #3.14# to approximate #pi# gives:
#V_c = 3.14 xx 8"in"^3#
#V_c = 25.12"in"^3#
The formula for the volume of a cylinder is:
#V_y = pir^2h#
Substituting #2"in"# for #r# and #6"in"# for #h# and calculating #V_y# gives:
#V_y = pi xx (2"in")^2 xx 6"in"#
#V_y = pi xx 4"in"^2 xx 6"in"#
#V_y = pi xx 24"in"^3#
Using #3.14# to approximate #pi# gives:
#V_y = 3.14 xx 24"in"^3#
#V_y = 75.36"in"^3#
The difference in the volume of the two shapes is:
#V_y - V_c#
#75.36"in"^3 - 25.12"in"^3 = 50.24"in"^3#
Another process to solve this would be to first subtract the formulas:
#V_y - V_c#
#pir^2h - pir^2h/3#
#pir^2(1h - h/3)#
#pir^2h(1 - 1/3)#
#pir^2h2/3#
Now substituting and calculating gives:
#3.14 xx (2"in")^2 xx 6"in" xx 2/3#
#3.14 xx 4"in"^2 xx 6"in" xx 2/3#
#3.14 xx 24"in"^3 xx 2/3#
#3.14 xx (48"in"^3)/3#
#3.14 xx 16"in"^3#
#50.24"in"^3#
