Question

for questions 5-8 use the following diagram:
diagram of a cylinder with h=12 and r=6
question 5: standard g.gmd.4
what would be the vertical cross section of this shape?
a. square
b. rectangle
c. circle
d. triangle
question 6: standard g.gmd.4
what would be the horizontal cross section of this shape?
a. circle
b. square
c. triangle
d. rectangle
question 7: standard g.gmd.4
how many dimensions do cross sections have?
a. 3
b. 1
c. 4
d. 2
question 8: standard g.gmd.4
what would be the dimensions of the vertical cross section through the center of the base?
a. 12 x 6
b. 6 x 6
c. 12 x 12
d. r = 6

Explanation:

Question 5

The shape is a cylinder with height \( h = 12 \) and radius \( r = 6 \). A vertical cross - section (cutting the cylinder vertically, parallel to its central axis) will have a height equal to the height of the cylinder (\( 12 \)) and a width equal to the diameter of the base (\( 2r=12 \))? Wait, no, wait. Wait, the radius is \( 6 \), so the diameter is \( 12 \), and the height of the cylinder is \( 12 \). Wait, no, the height of the cylinder is \( 12 \), and the diameter of the base is \( 2\times6 = 12 \). So a vertical cross - section (through the axis) will be a square? Wait, no, wait. Wait, the height of the cylinder is \( h = 12 \), and the diameter of the base is \( d=2r = 12 \). So when we take a vertical cross - section (parallel to the axis), the two vertical sides are equal to the height of the cylinder (\( 12 \)) and the two horizontal sides are equal to the diameter of the base (\( 12 \)), so it's a square? Wait, no, the options are square or rectangle. Wait, the height of the cylinder is \( 12 \), and the diameter of the base is \( 12 \) (since \( r = 6 \), \( d=12 \)). So the vertical cross - section (a plane cutting the cylinder vertically, passing through the axis) will have length \( 12 \) (height of cylinder) and width \( 12 \) (diameter of base), so it's a square. But wait, if we don't pass through the axis, would it be a rectangle? Wait, the standard vertical cross - section (usually the one through the axis) for a cylinder with \( h = 2r \) (here \( h = 12 \), \( r = 6 \), so \( h = 2r \)) will be a square. But let's re - examine. The cylinder has height \( h = 12 \) and radius \( r = 6 \). A vertical cross - section (perpendicular to the base, parallel to the axis) will have a height equal to \( h = 12 \) and a width equal to the diameter of the base \( d = 2r=12 \). So the vertical cross - section is a square. But wait, the options are a. Square, b. Rectangle, c. Circle, d. Triangle. So the answer should be a. Square? Wait, no, maybe I made a mistake. Wait, the height of the cylinder is \( 12 \), and the diameter of the base is \( 12 \), so the vertical cross - section (a rectangle with length and width both \( 12 \)) is a square. So the answer is a. Square.

A horizontal cross - section of a cylinder (cutting the cylinder parallel to its base) will be congruent to the base of the cylinder. The base of the cylinder is a circle (since the cylinder has a circular base with radius \( r = 6 \)). So the horizontal cross - section is a circle. The options are a. Circle, b. Square, c. Triangle, d. Rectangle. So the answer is a. Circle.

A cross - section is a two - dimensional figure. When we take a cross - section of a three - dimensional object, we are essentially looking at a "slice" of it, and this slice lies in a plane, so it has 2 dimensions. For example, a cross - section of a cylinder (a 3D object) is either a circle (2D) or a rectangle/square (2D). So cross - sections have 2 dimensions. The options are a. 3, b. 1, c. 4, d. 2. So the answer is d. 2.

Answer:

a. Square

Question 6