To determine the surface area of the rectangular prism formed by the given net, we need to find the areas of each of the individual faces and then add them up.
The net consists of:
- 2 squares with side lengths of 7 cm (top and bottom faces)
- 2 rectangles with dimensions 7 cm x 26 cm (front and back faces)
- 2 rectangles with dimensions 7 cm x 7 cm (side faces)
Calculating the areas of each face:
- Area of each square = side length x side length = 7 cm x 7 cm = 49 cm²
- Area of each 7 cm x 26 cm rectangle = length x width = 7 cm x 26 cm = 182 cm²
- Area of each 7 cm x 7 cm rectangle = 7 cm x 7 cm = 49 cm²
Now, calculating the total surface area:
- Top and bottom faces (2 x 49 cm²) = 98 cm²
- Front and back faces (2 x 182 cm²) = 364 cm²
- Side faces (2 x 49 cm²) = 98 cm²
Adding up all the areas:
98 cm² (top and bottom) + 364 cm² (front and back) + 98 cm² (sides) = 560 cm²
Therefore, the surface area of the rectangular prism formed by the given net is 560 cm².
The net below is used to form a rectangular prism. Using the net, determine the surface area of the figure.
7 cm
7 cm
7 cm
7 cm
26 cm
9 answers
The net on the left is used to form a rectangular prism. Using the net, Find the volume of the rectangular prism.
7 cm
7 cm
7 cm
7 cm
26 cm
7 cm
7 cm
7 cm
7 cm
26 cm
To determine the volume of the rectangular prism formed by the given net, we need to first identify the dimensions of the prism.
The net consists of:
- 2 squares with side lengths of 7 cm (top and bottom faces)
- 2 rectangles with dimensions 7 cm x 26 cm (front and back faces)
- 2 rectangles with dimensions 7 cm x 7 cm (side faces)
From the net, we can see that the dimensions of the rectangular prism are:
- Length = 26 cm
- Width = 7 cm
- Height = 7 cm
To find the volume of the rectangular prism, we multiply the length, width, and height together:
Volume = Length x Width x Height
Volume = 26 cm x 7 cm x 7 cm
Volume = 1274 cm³
Therefore, the volume of the rectangular prism formed by the given net is 1274 cubic centimeters.
The net consists of:
- 2 squares with side lengths of 7 cm (top and bottom faces)
- 2 rectangles with dimensions 7 cm x 26 cm (front and back faces)
- 2 rectangles with dimensions 7 cm x 7 cm (side faces)
From the net, we can see that the dimensions of the rectangular prism are:
- Length = 26 cm
- Width = 7 cm
- Height = 7 cm
To find the volume of the rectangular prism, we multiply the length, width, and height together:
Volume = Length x Width x Height
Volume = 26 cm x 7 cm x 7 cm
Volume = 1274 cm³
Therefore, the volume of the rectangular prism formed by the given net is 1274 cubic centimeters.
What is the approximate surface area of the cylinder? Round your answer to the nearest tenth.
Length: 20 in.
Width: 22 in.
Length: 20 in.
Width: 22 in.
The surface area of a cylinder is calculated by adding the areas of the two circular bases and the lateral surface area.
Given:
- The diameter of the cylinder is 20 inches, so the radius (r) is half of the diameter, which is 20 / 2 = 10 inches.
- The width of the cylinder (or the length of the lateral surface) is 22 inches.
1. Area of each circular base:
The area of a circle is πr^2, where r is the radius.
Using a radius of 10 inches:
Area of each circular base = π * (10)^2 = 100π square inches
2. Lateral surface area:
The lateral surface area of a cylinder is the circumference of the base multiplied by the height.
The circumference (C) is 2πr.
Using a radius of 10 inches:
Circumference = 2π * 10 = 20π inches
Lateral surface area = Circumference * height = 20π * 22 = 440π square inches
3. Total surface area:
Total surface area = 2 (Area of each circular base) + Lateral surface area
Total surface area = 2(100π) + 440π
Total surface area = 200π + 440π
Total surface area = 640π square inches
Approximating the value of π to 3.14 as an approximation:
Total surface area ≈ 640 * 3.14 = 2009.6 square inches
Rounded to the nearest tenth, the approximate surface area of the cylinder is 2009.6 square inches rounded to 1 decimal place would be 2010.0 square inches.
Given:
- The diameter of the cylinder is 20 inches, so the radius (r) is half of the diameter, which is 20 / 2 = 10 inches.
- The width of the cylinder (or the length of the lateral surface) is 22 inches.
1. Area of each circular base:
The area of a circle is πr^2, where r is the radius.
Using a radius of 10 inches:
Area of each circular base = π * (10)^2 = 100π square inches
2. Lateral surface area:
The lateral surface area of a cylinder is the circumference of the base multiplied by the height.
The circumference (C) is 2πr.
Using a radius of 10 inches:
Circumference = 2π * 10 = 20π inches
Lateral surface area = Circumference * height = 20π * 22 = 440π square inches
3. Total surface area:
Total surface area = 2 (Area of each circular base) + Lateral surface area
Total surface area = 2(100π) + 440π
Total surface area = 200π + 440π
Total surface area = 640π square inches
Approximating the value of π to 3.14 as an approximation:
Total surface area ≈ 640 * 3.14 = 2009.6 square inches
Rounded to the nearest tenth, the approximate surface area of the cylinder is 2009.6 square inches rounded to 1 decimal place would be 2010.0 square inches.
Find the volume of the cylinder. Round your answer to the nearest tenth.
Length: 20 in.
Width: 22 in.
Length: 20 in.
Width: 22 in.
To calculate the volume of a cylinder, you need to know the radius (r) and the height (h) of the cylinder. In this case, the radius is half of the width, and the height is given.
Given:
- Width (diameter) = 20 inches, so the radius (r) = 20 / 2 = 10 inches
- Height (h) = 22 inches
1. Calculate the volume using the formula:
Volume = πr^2h
2. Substitute the values into the formula:
Volume = π * (10)^2 * 22
Volume = π * 100 * 22
Volume = 2200π cubic inches
3. Calculate the approximate volume by substituting the value of π (approximately 3.14):
Volume ≈ 3.14 * 2200
Volume ≈ 6908 cubic inches
Therefore, the approximate volume of the cylinder is 6908 cubic inches when rounded to the nearest tenth.
Given:
- Width (diameter) = 20 inches, so the radius (r) = 20 / 2 = 10 inches
- Height (h) = 22 inches
1. Calculate the volume using the formula:
Volume = πr^2h
2. Substitute the values into the formula:
Volume = π * (10)^2 * 22
Volume = π * 100 * 22
Volume = 2200π cubic inches
3. Calculate the approximate volume by substituting the value of π (approximately 3.14):
Volume ≈ 3.14 * 2200
Volume ≈ 6908 cubic inches
Therefore, the approximate volume of the cylinder is 6908 cubic inches when rounded to the nearest tenth.
Quadrilateral HOME is similar to quadrilateral TRAP. Complete the statements below with the missing angle measures. Show work or explain your answer.
𝑚∠M = ____
𝑚∠M = ____
When two quadrilaterals are similar, it means that the corresponding angles are congruent, and the corresponding sides are proportional. Let's denote the angles in quadrilateral HOME as follows:
- ∠H = m
- ∠O = n
- ∠M = p
- ∠E = q
In quadrilateral TRAP, the corresponding angles to the ones above are matched as follows:
- ∠T = m
- ∠R = n
- ∠A = p
- ∠P = q
Since quadrilateral HOME is similar to quadrilateral TRAP, this means that the corresponding angles are equal: ∠H ≅ ∠T, ∠O ≅ ∠R, ∠M ≅ ∠A, and ∠E ≅ ∠P.
Therefore, 𝑚∠M = 𝑚∠A = p. So, 𝑚∠M = p.
- ∠H = m
- ∠O = n
- ∠M = p
- ∠E = q
In quadrilateral TRAP, the corresponding angles to the ones above are matched as follows:
- ∠T = m
- ∠R = n
- ∠A = p
- ∠P = q
Since quadrilateral HOME is similar to quadrilateral TRAP, this means that the corresponding angles are equal: ∠H ≅ ∠T, ∠O ≅ ∠R, ∠M ≅ ∠A, and ∠E ≅ ∠P.
Therefore, 𝑚∠M = 𝑚∠A = p. So, 𝑚∠M = p.
1 answer