Since it is given that both prisms have the same height and volume, the answer is option D. The horizontal cross-sections of the prisms at the same height must have the same area.
A solid figure is one which has surface area and volume. Examples are prisms, cube, cuboid etc. Thus cones and pyramids are solid figures.
From the given question,
Volume of a cone, V = [tex]\frac{1}{3}[/tex][tex]\pi r^{2} h[/tex]
where r is its radius, and h its height
also,
Volume of a pyramid, V = [tex]\frac{1}{3}[/tex] lwh
where l is its length, w is the base width and h is its height.
Given that: i. volume of cone = volume of pyramid
ii. height of cone = height of pyramid
Then,
[tex]\frac{8}{3}[/tex][tex]\pi r^{2}[/tex] = [tex]\frac{8}{3}[/tex]lw
[tex]\pi r^{2}[/tex] = lw
Thus it can be deduced that at the same height, the horizontal cross section of the prisms have equal area. So that option D is the appropriate answer to the given question.
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