The rectangular prism is a three dimensional figure formed by six rectangular faces. It's volume is given by the product of it's three dimensions. The calculation for the volume of this prism is shown bellow:

volume = width*height*length

volume = 9*10*4

volume = 360 cm^3

The volume of the prism is 360 cm^3.

7 0

3 years ago

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The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y

Ivahew [28]

The area of an equilateral triangle of side "s" is s^2*sqrt(3)/4. So the volume of the slices in your problem is

(x - x^2)^2 * sqrt(3)/4.

Integrating from x = 0 to x = 1, we have

[(1/3)x^3 - (1/2)x^4 + (1/5)x^5]*sqrt(3)/4

= (1/30)*sqrt(3)/4 = sqrt(3)/120 = about 0.0144.

Since this seems quite small, it makes sense to ask what the base area might be...integral from 0 to 1 of (x - x^2) dx = (1/2) - (1/3) = 1/6. Yes, OK, the max height of the triangles occurs where x - x^2 = 1/4, and most of the triangles are quite a bit shorter...

8 0

4 years ago