Question

Mitchell poured the contents of a completely filled cone into an empty cylinder, and the cylinder became two-thirds full. The cylinder had a radius of 5 cm and a height of 15 cm. What were possible dimensions of the cone? Use 3.14 to approximate pi.
a. h = 5 cm; r = 15 cm
b. h = 7.5 cm; r = 10 cm
c. h = 10 cm; r = 7.5 cm
d. h = 15 cm; r = 5 cm

Answer 1

Answer: B. h = 7.5 cm ; r = 10 cm
Given:
Cylinder 
Cone

Volume of Cylinder = π r² h
= 3.14 * (5cm)² * 15cm
= 3.14 * 25cm² * 15cm
= 1,177.50 cm³

Volume of the cone = 1,177.50 cm³ * 2/3
= 2355 cm³ ÷ 3 
= 785 cm³

Volume of the cone = π r² h/3

a) 3.14 * 15² * 5/3 = 1177.50 cm³
b) 3.14 * 10² * 7.5/3 = 785 cm³
c) 3.14 * 7.5² * 10/3 = 588.75 cm³
d) 3.14 * 5² * 15/3 = 392.50 cm³