Question

You wish to package a spherical globe inside a cubical box . The diameter of the globe is 30 centimeters . How much empty space is there inside the rectangular prism ( i.e. how much space is there between the prism and the globe ) ? Hint Volume Rectangular Prism is L x W x H

Answer 1

The empty inside the box is 12,870 cubic centimeters, approximately.

Explanation:

Givens

• The diameter of the globe (sphere) is 30 centimeters,
• The box must has dimensions 30x30.

We need to find each volume to subtract them.

`V_(box)=(30cm)^(3)= 27,000 \ cm^(3)`

`V_(sphere)=(4)/(3) \pi (15cm)^(3) \approx 14,130 \cm^(3)`

The difference betweem the box and the sphere is

`\Delta V=27,000 - 14,130 = 12,870 \ cm^(3)`

Therefore, the empty inside the box is 12,870 cubic centimeters, approximately.