Question

Propane is stored in a cylindrical tank with a diameter of 15 inches and a height of 48 inches. Which equation could be used to determine the radius of a spherical tank with the same volume?

Answer 1

To find the radius of a spherical tank with the same volume as a given cylindrical propane tank, equate the volume of the cylinder to the volume of the sphere and solve for the sphere's radius. The cylindrical volume formula πr²h, where r is half the diameter of 15 inches, is set equal to ⅜πr_s³, and the spherical radius r_s is isolated and solved.

Step-by-step explanation:

The equation to determine the radius of a spherical tank with the same volume as a cylindrical propane tank can be found by equating the volume formulas for both shapes and solving for the radius of the sphere. The cylinder's volume formula is V = πr²h, where r is the cylinder's radius and h is its height. The volume of a sphere is given by the formula V = ⅜πr³, where r is the sphere's radius. Given the diameter of the cylinder is 15 inches, its radius is 7.5 inches.

To find the radius r of the spherical tank, set the volume of the cylinder equal to the volume of the sphere and solve for the spherical radius:

• Find the volume of the cylinder: V_cylinder = π(7.5 inches)²(48 inches).
• Equate the two volumes and solve for the spherical radius r_s: V_cylinder = ⅜πr_s³.
• Rearrange and solve for r_s: r_s = ∛(³√(V_cylinder/⅜π)).

Answer 2

Step-by-step explanation:

remember. the radius is always half the diameter.

volume of a cylinder

pi × r² × height

pi×7.5²×48 = pi×56.25×48 = 8,482.300165... in³

volume of a sphere

4/3 × pi × r³

and that volume should be the same as the cylinder. so,

4/3 × pi × r³ = pi×56.25×48

4/3 × r³ = 56.25 × 48

1/3 × r³ = 56.25 × 12

r³ = 56.25 × 36 = 7.5² × 6² = (7.5×6)² = 45² = 2025

`r = \sqrt[3]{2025}`

which would be 12.65148998... in.