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.
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