Question

Correct Answers only please!

When estimating the number of spheres contained in a prism we should account for the empty space between the spheres. To do this we find 190% of the volume of the sphere and use that value in our estimation.


If gumballs have a 2 inch diameter, what should we use as the volume of each gumball in our calculation? (Round your answer to the nearest tenth)



A. 4.2 cubic inches


B. 8.0 cubic inches


C. 33.5 cubic inches


D. 5280 cubic inches

Answer 1

A. 4.2 in³

Explanation:

As provided, the volume of a sphere is:

V = 4/3 π r³

where r is the radius of the sphere.

We're given that the diameter of the sphere is 2 inches. The radius is half the diameter, so the radius is 1 inch. Therefore, the volume of the sphere is:

V = 4/3 π (1 in)³

V ≈ 4.2 in³

Answer 2

B. 8.0 cubic inches

Explanation:

You need to find 190% of the volume of a gumball which is a sphere.

To find 190% of a quantity, multiply the quantity by 1.9.

volume of sphere = (4/3)(pi)(r^3)

diameter = d = 2 in.

radius = r = (1/2)d = (1/2)(2 in.) = 1 in.

volume of sphere = (4/3)(3.14159)(1 in.)^3 = 4.189 in.^3

The volume of a gumball is 4.189 in.^3

Now we need 190% of that volume.

190% of volume of sphere = 1.9 * volume = 1.9 * 4.189 in.^3 = 7.959 in.^3

Rounded to the nearest tenth, the volume is

B. 8.0 cubic inches