Question

What is the shape of the cross-section formed when a plane containing line AC and line EH intersects this cube? What is the area of the cross-section? In two or more complete sentences, explain how you were able to determine the shape and area of the cross-section. Be sure to include the properties of quadrilaterals and the mathematical computations necessary to support your answers

https://treca.owschools.com/media/g_geo_ccss_2016/8/img_geou08l15_3.gif

Answer 1

try to imagine this shape sliced through the cube diagonally.

now consider the triangle EGH at the bottom


you can use the pythagorean theorem since we have a right triangle with legs GH and EG, and hypotenuse EH

leg^2 + leg^2 = hypotenuse^2

Answer 2

the hypotenuse of that triangle is the bottom side of the purple cross-section. now, the height of the cross section (a.k.a sides AE and CH) are equal to 4 because these are just side lengths of the cube

now for the top side, the length of AC should be equivalent to EH via symmetry of the cube

Answer 3

finally, your end result for the cross-section will be a 4-sided shape with four right angles, two pairs of opposite congruent parallel sides. however, all four sides are *not* equal to each other. with that said look at the types of quadrilaterals and try to see which one is the best fit for this description.

Answer 4

thanks

Answer 5

A sculptor is planning to order a cylinder of composite stone to sculpt a full-sized person. The figure will be 6 feet tall, and 2’ at the longest diameter. The composite stone weighs 50 pounds per cubic foot. About how much will the smallest cylinder weigh that the sculptor can order to make his statue?

Answer 6

ah I didn't see this until today :S
first step is to calculate the volume of a cylinder that would fit exactly around the statue

V = pi * r^2 * h
where r = the radius, h = the height
they give you height and diameter, so you can just divide diameter/2 to get radius

after you calculate the volume, multiply by the 50lbs per cubic foot to get the weight