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A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the height of the prism is placed inside the prism, as shown in the figure.

The volume of the space outside the pyramid but inside the prism is
cubic centimeters.

Respuesta :

sylvain96

Answer:

250 cubic cm

Step-by-step explanation:

First step is to measure the volume of the rectangular prism... which is easy... it's the width * length * height.  Since we have a square base, the width and length are the same: 5 cm.  The volume is then: 5 * 5* 12 = 300 cubic cm.

The volume of a pyramid is obtained by the following formula:

V = (1/3) * base_area * height

We have the base area (5 * 5 = 25) and we have the height: 6 cm (half of 12 cm).

So, the volume of the pyramid is:

V = (1/3) * 25 * 6 = (1/3) * 150 = 50 cubic cm

The volume inside the prism but OUTSIDE the pyramid is then the volume of the prism (300 cubic cm) - the volume of the pyramid (50 cubic cm), so 250 cubic cm.

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