Question

1. The edge lengths of a right rectangular prism are

Answer 1

Answer:

1) 324 cubes can be fitted into the rectangular prism.

2) 1/12 cubic ft.

3) 125 cubes can be fitted into the rectangular prism.

Step-by-step explanation:

1)

The edge lengths of the prism are given as:

1/2 meter, 1/2 meter and 3/4 meter.

The formula for finding the volume of a rectangular prism is the following: Volume = Length×Height×Width, or V = L×H×W.

so here let L=1/2 meter, B=1/2 meter and H=3/4 meter

Hence, V=(1/2)×(1/2)×(3/4)=3/16 cubic meters.

Now let 'n' cubes can be fitted inside this rectangular prism.

Let 'v' denotes the volume of 1 cube.

Volume of a cube with side length 's' units is given by:

$v=s^3 cubic units.$

Here s=1/12 meter

Hence, volume of cube (v)=(1/12)×(1/12)×(1/12)=1/1728 cubic meter

Now V=n×v

$n=\dfrac{V}{v}\\\\n=\dfrac{\dfrac{3}{16}}{\dfrac{1}{1728}}\\\\\\n=\dfrac{3\times 1728}{16}\\\\n=324$

Hence, 324 cubes can be fitted into the given rectangular pyramid.

2)

The base of a rectangular prism has an area of  1/8 square feet.

This means let the rectangular base has length L and base B such that L×B=1/8 square feets.

also height (H) of the rectangular prism=2/3 ft.

Hence volume of rectangular prism= L×B×H=(1/8)×(2/3)=1/12 cubic ft.

3)

The edge lengths of the prism are given as:

2/3 meter, 1/4 meter and 3/4 meter.

The formula for finding the volume of a rectangular prism is the following: Volume = Length×Height×Width, or V = L×H×W.

so here let L=2/3 meter, B=1/4 meter and H=3/4 meter

Hence, V=(2/3)×(1/4)×(3/4)=1/8 cubic meters.

Now let 'n' cubes can be fitted inside this rectangular prism.

Let 'v' denotes the volume of 1 cube.

Volume of a cube with side length 's' units is given by:

$v=s^3 cubic units.$

Here s=1/10 meter

Hence, volume of cube (v)=(1/10)×(1/10)×(1/10)=1/1000 cubic meter

Now V=n×v

$n=\dfrac{V}{v}\\\\n=\dfrac{\dfrac{1}{8}}{\dfrac{1}{1000}}\\\\\\n=\dfrac{1000}{8}\\\\n=125$

Hence, 125 cubes can be fitted into the given rectangular pyramid.