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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

Respuesta :

Answer:

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

Step-by-step 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.

[tex]V_{box}=(30cm)^{3}= 27,000 \ cm^{3}[/tex]

[tex]V_{sphere}=\frac{4}{3} \pi (15cm)^{3} \approx 14,130 \cm^{3}[/tex]

The difference betweem the box and the sphere is

[tex]\Delta V=27,000 - 14,130 = 12,870 \ cm^{3}[/tex]

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

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