Options :
A. A cylinder in which h = 1 and d = 6 has a volume of 27π in3; therefore, Wilson is correct.
B. A cylinder in which h = 3 and d = 6 has a volume of 27π in3; therefore, Wilson is incorrect.
C. A cylinder in which h = 1 and d = 6 has a volume of 9π in3; therefore, Wilson is incorrect.
D. A cylinder in which h = 3 and d = 6 has a volume of 9π in3; therefore, Wilson is correct.
Answer: B. A cylinder in which h = 3 and d = 6 has a volume of 27π in3; therefore, Wilson is incorrect
Step-by-step explanation:
Given the following :
The volume of cone = 9π in^3
Diameter= 6 in
Wilson's statement: Wilson states that a cylinder with the same height and diameter has the same volume
Firstly:
Let's calculate the height of the cone
The volume(V) of a cone = (1/3)πr^2h
h = height, r = radius = diameter/2 = 6/2 = 3 in
V = (1/3) * π * 3^2 * h
9π = 1/3 * π * 9 * h
9π = 9πh / 3
3 * 9π = 9πh
Divide both sides by 9π
h = 3
Now calculating the volume of a cylinder:
Volume(V) of a cylinder = πr^2h
V = π * 3^2 * 3
V = π * 9 * 3
V = 27π in^3
Both volumes are different, therefore Wilson is incorrect
Answer:
B. A cylinder in which h = 3 and d = 6 has a volume of 27π in3; therefore, Wilson is incorrect.
