Question

A cone has a volume of 50π in3 and a diameter of 10 in. Wilson states that a cylinder with the same height and diameter has the same volume. Which statement explains whether or not Wilson is correct? A cylinder in which h = 2 and d = 10 has a volume of 50π in3; therefore, Wilson is incorrect. A cylinder in which h = 6 and d = 10 has a volume of 50π in3; therefore, Wilson is incorrect. A cylinder in which h = 2 and d = 10 has a volume of 150π in3; therefore, Wilson is incorrect. A cylinder in which h = 6 and d = 10 has a volume of 150π in3; therefore, Wilson is incorrect.

Answer 1

Answer:

A cylinder in which h = 6 and d = 10 has a volume of 150π in³ ; therefore, Wilson is incorrect ⇒ last answer

Step-by-step explanation:

* Lets revise the volume of the cone and the cylinder

- The volume of cone is 1/3 πr²h, where r is its radius and h is its height

- The volume of the cylinder is πr²h

* Lets solve the problem

∵ The cone has a volume 50π inches³

∵ The diameter of the cone is 10 inches

∵ The diameter is twice the radius

∴ 2r = 10 ⇒ divide both sides by 2

∴ r = 5

∵ The rule of the volume of the cone = 1/3 πr²h

∴ 50π = 1/3 π (5²)h

∵ 50π = 1/3 (25π)h ⇒ divide both sides by 25π

∴ 2 = 1/3 h ⇒ multiply both sides by 3

∴ 6 = h

∴ The height of the cone is 6 inches

- The cylinder has the same diameter and the same height of the cone

∵ The diameter of the cone = 10 inches

∵ The height of the cone = 6 inches

∴ The diameter of the cylinder is 10 inches

∴ The height of the cylinder is 6 inches

∵ The rule of the volume of the cylinder is πr²h

∵ The radius of the cylinder = 10/2 = 5 inches

∴ The volume of the cylinder = π(5²)(6) = 150π inches³

* The volume of the cylinder not equal the volume of the cone

∴ A cylinder in which h = 6 and d = 10 has a volume of 150π in³ ;

   therefore, Wilson is incorrect.

Answer 2

Answer: A cylinder in which h = 6 and d = 10 has a volume of 150π in3; therefore, Wilson is incorrect.

Step-by-step explanation: I took the test and the answer is 100% correct.