Question

What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432c * m ^ 2 ?(1 point)

cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

Given:
Width = 9 cm
Height = 9 cm
Surface area = 432 cm^2

Substitute the given values into the formula:
2(9)(9) + 2(9)(l) + 2(9)(l) = 432
162 + 18l + 18l = 432
162 + 36l = 432
36l = 270
l = 7.5

Therefore, the missing length of the rectangular prism is 7.5 cm.

Answer 2

Fill in the blanks to complete the formula for the surface area of a triangular prism.

The surface area of a triangular prism is S. A.= Box+ (S_{1} + S_{2} + S_{3}) Box

Answer 3

[AI-generated answer — Bot GPT 3.5]

The surface area of a triangular prism consists of the area of the two triangular bases and the area of the three rectangular sides. The formula for the surface area of a triangular prism can be completed as:

\(S.A.= Area\; of\; the\; two\; triangular\; bases + (S_1 + S_2 + S_3)\)

Answer 4

10.6 cm

Item 13

10 cm

Item 14

Item 15

7

12 cm

14 cm

What is the surface area of the rectangular pyramid?

(1 point)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the surface area of a rectangular pyramid, we need to calculate the area of the base and the area of the three triangular faces separately.

Given:
Base length: 10 cm
Base width: 14 cm
Slant height: 10.6 cm (height of the pyramid)
Side lengths of the triangular faces: 7 cm, 12 cm, and 14 cm

1. Calculate the area of the base:
Area = Base length x Base width
Area = 10 cm x 14 cm
Area = 140 cm^2

2. Calculate the area of each triangular face using the formula for the area of a triangle (0.5 x base x height):
Area of the first triangular face = 0.5 x 7 cm x 10.6 cm
Area of the first triangular face = 37.1 cm^2

Area of the second triangular face = 0.5 x 12 cm x 10.6 cm
Area of the second triangular face = 63.6 cm^2

Area of the third triangular face = 0.5 x 14 cm x 10.6 cm
Area of the third triangular face = 74.2 cm^2

3. Add the areas of the base and the three triangular faces to find the total surface area:
Total surface area = Area of base + Sum of areas of the three triangular faces
Total surface area = 140 cm^2 + (37.1 cm^2 + 63.6 cm^2 + 74.2 cm^2)
Total surface area = 140 cm^2 + 175.9 cm^2
Total surface area = 315.9 cm^2

Therefore, the surface area of the rectangular pyramid is 315.9 cm^2.

Answer 6

What is the surface area of the figure?

(1 point)

f * t ^ 2

8 ft.

15 ft.

20 ft.

8 ft.

8 ft.

12 ft.

Answer 7

[AI-generated answer — Bot GPT 3.5]

To calculate the surface area of the figure provided, we need to identify the individual faces and then calculate their areas before adding them together.

Given:
Three pairs of rectangular faces, each pair with dimensions:
1. 8 ft by 15 ft
2. 8 ft by 8 ft
3. 8 ft by 12 ft

1. Calculate the areas of the rectangular faces:
1st pair of faces:
Area = 2(8 ft x 15 ft) = 2(120 ft^2) = 240 ft^2

2nd pair of faces:
Area = 2(8 ft x 8 ft) = 2(64 ft^2) = 128 ft^2

3rd pair of faces:
Area = 2(8 ft x 12 ft) = 2(96 ft^2) = 192 ft^2

2. Add the areas of the three pairs of faces:
Total surface area = 240 ft^2 + 128 ft^2 + 192 ft^2
Total surface area = 560 ft^2

Therefore, the surface area of the figure is 560 ft^2.

Answer 8

In Los Cabos, Mexico, there is a big sculpture of block letters that welcomes you. The image shows the letter C. What is its surface area?

(1 point)

f * t ^ 2

Answer 9

[AI-generated answer — Bot GPT 3.5]

The surface area of a block letter C can be calculated by determining the areas of each of the six faces of the block letter C and then summing them up.

Given:
The block letter C has dimensions:
- Width (w) = 15 ft
- Height (h) = 20 ft
- Thickness (t) = 8 ft

Since the letter C has a curved shape, we need to consider the outer surface area of the letter C.

For a block letter C, we need to consider three rectangular faces (front, top, and side), and the other three faces are the inner surfaces that are not visible.

1. Calculate the area of the front face (facing outward):
Area of front face = width x height = 15 ft x 20 ft = 300 ft^2

2. Calculate the area of the top face:
Area of top face = width x thickness = 15 ft x 8 ft = 120 ft^2

3. Calculate the area of the side face:
Area of side face = height x thickness = 20 ft x 8 ft = 160 ft^2

4. Add up the areas of the front, top, and side faces to get the total surface area:
Total surface area = 300 ft^2 + 120 ft^2 + 160 ft^2 = 580 ft^2

Therefore, the surface area of the block letter C is 580 ft^2.