Answered

A globe had a diameter of 17.8. It fits inside a cube-shaped box that has a side length of 17.8. What is the volume of the space inside the box that is not taken up by the globe?



Use 3.14 as pie. Round to the nearest hundredth

Verified Answer :

Answer:

Step-by-step explanation:

volume of box       -        volume of sphere    = unused space

L X W X H              -         4/3 pi r^3

17. 8 x 17.8 x 17.8   -   4/3 ( 3.14) ( 17.8/2)^3   = 2688.28 units^3

regalmocha17

Answer:

Volume not taken up by the globe is 2688.28 units^3.

Step-by-step explanation:

To solve this problem, we require two formulas: the volume of a sphere and the volume of a cube. They are..

\(V_{c} = a^3 \\V_{s} = \frac{4}{3} \pi r^3\)

Our given values are:

globe diameter of 17.8 units

cube side length of 17.8 units

To, get the volume of the sphere, we need the radius which can be obtained by dividing the diameter by 2.

17.8/2 = 8.9

radius of globe = 8.9 units

Now we can solve for the volumes of both objects.

\(V_{c} = a^3 \\V_{c} = 17.8^3 \\V_{c} = 5639.752 units^3\)

\(V_{s} = \frac{4}{3} \pi (r^3)\\V_{s} = \frac{4}{3} \pi (8.9^3)\\V_{s} = \frac{4}{3} \pi (r^3) \\V_{s} = 2951.470213 units^3\)

\(V_{nt} = 5639.752 - 2951.470213 \\V_{nt} = 2688.281787 \\\)

Round to nearest hundredth.

V = 2688.28