Question

A cylinder with a radius of 4 units and a rectangular prism have equal heights, and every plane parallel to the bases intersects both solids in cross-sections of equal area.

A cylinder with a radius of 4 units and a rectangular prism have equal heights.

A rectangular cross section with a length of 8 units is marked on the prism, parallel to the base.

If the length of a rectangular cross-section of the prism is 8 units, then the width of a rectangular cross-section of the prism is
units. Write your answer in terms of π .

Answer 1

The width of the rectangular cross-section of the prism is; 2π units.

Area of a circle and Rectangle

From the task content;

• By observation, it follows that the area of a cross section of the cylinder is equal to the area of the cross-section of the rectangular prism.

From the problem statement above; it follows that;

• πr² = l×w.

On this note;

• (π) × 4² = 8 × w

• w = (16× π)/8

width, w = 2π units

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