Question

A right rectangular prism has base dimensions of 3 inches by 12 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches. A right rectangular prism has base dimensions of 3 inches by 12 inches. An oblique rectangular prism has base dimensions of 9 inches by 4 inches. If the prisms are the same height, how do their volumes compare? The volumes are equal, because the bases are congruent. The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal. The volumes are not equal, because their horizontal cross-sectional areas are not the same at every level.

Answer 1

The volume of right rectangular prisms and oblique rectangular prisms are 36x that are equal.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Volume is given by

$\rm volume = base \ area * height$

If the prisms are of the same height (x). Then

A right rectangular prism has base dimensions of 3 inches by 12 inches. Then the volume (V₁) will be

$\rm V_1 = 3*12*x\\\\V_1 = 36x$

An oblique rectangular prism has base dimensions of 4 inches by 9 inches. Then the volume (V₁) will be

$\rm V_2 = 4*9*x\\\\V_2 = 36x$

A right rectangular prism has base dimensions of 3 inches by 12 inches. Then the volume (V₁) will be

$\rm V_3 = 3*12*x\\\\V_3 = 36x$

An oblique rectangular prism has base dimensions of 9 inches by 4 inches. Then the volume (V₁) will be

$\rm V_4 = 9*4*x\\\\V_4 = 36x$

The volume of right rectangular prisms and oblique rectangular prisms are 36x that are equal.

More about the geometry link is given below.

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