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A rectangular pyramid fits exactly on top of a rectangular prism. The prism has length 24 cm, width 3cm, and height 12 cm, and the pyramid has height 21 cm. Find the volume of the composite space figure.

Respuesta :

carlosego
To solve this prolem you must apply the proccedue shown below:

 1. You must apply the formula for calculate the volume of a rectangular prism and the formula for calculate the volume of a rectangular pyramid:

 - Volume of the rectangular prism:

 V1=lwh

 Where l is the length, w i the width and h is the height

 V1=(24 cm)(3 cm)(12 cm)
 V1=864 cm^3

 - Volume of the rectangular pyramid:

 V2=lwh/3

 Where l is the length, w is the width and h is the height

 V2=(24 cm)(3 cm)(21 cm)/3
 V2=504 cm^3

 -The volume of the figure is:

 Vt=V1+V2
 Vt=1368 cm^3

 The answer is: 1368 cm^3

 
nuhulawal20

Given the values of the lengths, widths and heights of the rectangular prism and the rectangular pyramid, the volume of the composite figure is 1368cm³.

What is a rectangular prism and pyramid?

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

A rectangular pyramid is a three-dimentional object with a rectangular shaped base and triangular shaped faces that correspond to each side of the base.

The volume of rectangular pyramid is expressed as;

V = (1/3) × l × w × h

Where l is the base length, w is the base width and h is the height of the pyramid.

Given the data in the question.

For the rectangular prism;

  • Length l = 24cm
  • Width w = 3cm
  • Height h = 12cm

For the rectangular pyramid;

  • Length l = 24cm
  • Width w = 3cm
  • Height h = 21cm

The volume of the composite figure will be;

V = volume of the rectangular prism + volume of the rectangular pyramid

V = ( w × h × l ) +  ( (1/3) × l × w × h )

V = ( 24cm × 12cm × 3cm ) +  ( (1/3) × 24cm × 3cm × 21cm )

V = 864cm³ + 504cm³

V = 1368cm³

Therefore, given the values of the lengths, widths and heights of the rectangular prism and the rectangular pyramid, the volume of the composite figure is 1368cm³.

Learn more about volume of pyramids here: brainly.com/question/21308574

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