Question

A rectangular pyramid is sliced so the cross section is perpendicular to its base but does not pass through its vertex.

What is the shape of the cross section?
square
rectangle
trapezoid
triangle

A sphere is sliced so that the cross section does not intersect the center of the sphere.

What is the shape of the cross section?
circle
semicircle
square
rectangle


What is the area of a cross section that is parallel to face CDHG ?
Enter your answer in the box. ( picture)


What is the area of the two-dimensional cross section that is parallel to face ABC ?
Enter your answer in the box. ( picture)

This rectangular prism is intersected by a plane that contains points D, E, K, and L.
What is the perimeter of the cross section?
Enter your answer in the box. Round only your final answer to the nearest tenth. (picture)

Answer 1

Problem 1) 

A trapezoid forms. See "figure1" in the attachments to get a visual idea of what I mean.

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Problem 2) 

We get a circle that forms but this circle is has a smaller radius compared to the radius of the sphere. See figure 2 (attached)

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Problem 3) 

Area of bottom face CDHG = length*width = 36*12 = 432

Any face parallel to this will have the same area. The same applies to any parallel cross section.

Answer: 432 square cm

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Problem 4) 

EF = 12 ft which runs parallel to BC, so BC = 12 ft as well

area of triangle ABC = (0.5)*(base)*(height)
area of triangle ABC = (0.5)*(BC)*(AB)
area of triangle ABC = (0.5)*(12)*(5)
area of triangle ABC = 30

Any cross section parallel to face ABC will also have the same area.

Answer: 30 square feet

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Problem 5) 

Using the pythagorean theorem we find that EK is roughly 6.40312 meters long

a^2 + b^2 = c^2
4^2 + 5^2 = c^2
c^2 = 41
c = sqrt(41)
c = 6.40312

LD = EK as they are parallel
DE = LK for the same reason

DE = 12
EK = 6.40312
LK = 12
LD = 6.40312

The perimeter of plane DEKL is roughly
P = (DE) + (EK) + (KL) + (LD)
P = (12) + (6.40312) + (12) + (6.40312)
P = 36.80624
P = 36.8

Answer: 36.8

Answer 2

A. A rectangular pyramid that is sliced such that its cross-section is perpendicular to the base (without passing through its vertex will yield a triangle. For this question, therefore, the answer is D - Triangle.

What is a vertex?

This refers to the points of the corner of a polygon or a polyhedron. It is formed when the edges of the object intersect.

B. The shape of a cross-section that is cut out of a sphere without going through the center is called a Circle. The answer, in this case, is A.

C. The area of the cross-section that is parallel to the area CDHG is given as:

12cm x 36cm = 432cm

. This is because the area in question is a rectangle. The formula for the area of a rectangle is given as Lenght multiplied by breadth.

D. The section that is parallel to face ABC in the picture is labeled DEF. That area is a right-angle triangle. The area of a right-angle triangle is given as:

1/2 (base x height) or 1/2 (ED x FE)

This translates to:

(5ft x 12ft)/2

= 60ft/2

= 30ft.

E. The shape in question is a rectangular prism whose height is 5 meters, width 4 meters and length is 12 meters.

The length of the diagonal EK translates to $\sqrt((5^{2} )+ (4^{2}))$

this gives us $\sqrt{} (25+16) or \sqrt{} 41$

≅ 6.403

Hence, the perimeter = 2 x (12 + 6.403)

= 2 x (18.403)

≅ 36.8 m or 37 meters.

See the link below for more calculations about shapes:

https://brainly.com/question/12580764