1. You have a solid cube of dough. Consider the cross sections that are formed when you slice into the cube as described. Draw each slice to help you describe the resulting cross section. Descriptions of each cross section must include the name of the shape formed.
(a) A slice through the center, parallel to a side.
(b) A slice that cuts diagonally through the left top edge and the right bottom edge.
(c) The cube’s original side length is 4.5 cm. What is the area of a cross section sliced perpendicular to the base?(Question 2: 10 points)

2. Leo made a container to store his camping gear. The container is in the shape of a rectangular prism. The container has material covering all six sides.

(a) What is the capacity of the container?
(b) How much material was used to make the container (surface area)?

answer:

(a)

A square is formed.

(b)

A rectangle is obtained.

(c)

A triangle is formed.

Step-by-step explanation:

We have to tell different cross sections that are obtained on slicing a cube in different ways.

(a)

A slice through the center, parallel to a side.

( As the slicing is done parallel to the base and the cube is sliced from the center hence we will obtain the figure similar to it's base or top i.e. square)

Hence, a square is obtained.

( As the sides of a cube are squares)

(b)

A slice that cuts through the left top edge and the right bottom edge.

i.e. the slicing is done across the diagonal of a cube hence we will obtain the rectangle with dimension as one side which has measure same as the diagonal of a cube and the other side which has measure same as the measure of side of square.

Hence, a rectangle is obtained.

(c)

A slice that cuts across a corner through three sides of the cube.

This slicing will form a triangle whose three sides are the three sides of the cube through which slicing is done.

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Step-by-step explanation:

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

answer: 7270

step-by-step explanation: