Question

Which correctly describes a cross section of the cube below? Check all that apply.

A cube with 4 centimeter sides.

A cross section parallel to the base is a square measuring 4 cm by 4 cm.

A cross section parallel to the base is a rectangle measuring 4 cm by greater than 4 cm.

A cross section perpendicular to the base through the midpoints of opposite sides is a rectangle measuring 2 cm by 4 cm.

A cross section perpendicular to the base through the midpoints of opposite sides is a square measuring 4 cm by 4 cm.

A cross section that passes through the entire bottom front edge and the entire top back edge is a rectangle measuring 4 cm by greater than 4 cm.

Answer 1

B,E and F

Explanation:

• (B)A cross section parallel to the base is a square measuring 4 cm by 4 cm.

Since a cube has equal base length, any cross section parallel to the base will also have an equal base length.

• (E)A cross section perpendicular to the base through the midpoints of opposite sides is a square measuring 4 cm by 4 cm.

Since a cube has equal side lengths, any cross section parallel to the side will also have an equal base length.

• (F)A cross section that passes through the entire bottom front edge and the entire top back edge is a rectangle measuring 4 cm by greater than 4 cm.

Using Pythagoras Theorem

`4^2+4^2=4√(2)>4`

There the cross section will be a rectangle which measures
`4√(2)\:cm\:by\:4\:cm`