Question

Gold in the form of solid cylinders will be molded into solid blocks. Each cylinder has a diameter of 6.19 cm and a height of 6 cm. Each solid block will have a volume of 360 cm3. How many cylinders of gold will it take to mold one block of gold?

Answer 1

Most of the information's required for solving the question is already given.
Height of each cylinder (H) = 6 cm
Diameter of each cylinder (D) = 6.19 cm
Then
Volume of each cylinder = πD²H / 4
                                       = [3.14 * (6.19)^2 * 6] / 4
                                       = [3.14 * 38.32 * 6] / 4
                                       = 721.88/4
                                       = 180.47 cubic centimeter
Volume of each solid block of gold = 360 cm^3
Then
Number of cylinders required = 360/180.47
                                               = 1.99
                                               = 2
From the above deduction, we can conclude that 2 cylinders will be required.

Answer 2

First, solve for the volume (V) of each cylinder by the equation,
                                     V = πd²h / 4
where d and h are diameter and height, respectively. Substituting the given values,
                                     V = π(6.19 cm)² x (6 cm) / 4 = 180.56 cm³
To determine the number of cylinders needed, divide the volume of the solid block by the volume of the cylinder,
                                       n = 360 cm³ / 180.56 cm³ = 1.99
Thus, approximately 2 cylinders are needed to mold one block of gold.