Question

A 40-inch by 40-inch piece of marble that is 72 inches long is cut
lengthwise along its diagonal. Find the area of the cross section formed
by the cut. Round each answer to the nearest whole number.

Answer 1

Answer:

$3296 in.^2$

Step-by-step explanation:

The initial shape of the piece of marble is a parallelepiped, of sides:

$w=40 in.$

$h=40 in.$

$L=72 in.$

Then, this piece of marble is cut along the diagonal. This means that its volume will halve, and the new cross section will have a shape of a rectangle, where:

- The base of the rectangle is the diagonal of the original parallelepiped

- The height of the rectangle is the height of the original parallelepiped

So we have:

- The diagonal is given by Pythagorean's theorem, so

$d=\sqrt{L^2+w^2}=\sqrt{72^2+40^2}=82.4 in.$

So, this is the base of the rectangle:

$b=d=82.4 in.$

while the height is

$h=40 in.$

So the cross-sectional area of this rectangle is:

$A=b\cdot h =(82.4)(40)=3296 in^2$