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Example Question - rectangular prism

Here are examples of questions we've helped users solve.

Finding the Volume of a Rectangular Prism

El volumen \( V \) de un prisma rectangular se calcula mediante la fórmula: \( V = largo \times ancho \times alto \) En este caso, todos los lados son \( 6 \, \text{cm} \): \( V = 6 \, \text{cm} \times 6 \, \text{cm} \times 6 \, \text{cm} \) \( V = 216 \, \text{cm}^3 \)

Calculating Surface Area of Composite 3D Figure

To find the surface area of the 3D figure provided in the image, you need to calculate the area of each visible surface and then add them all together. The figure is a composite solid made up of two rectangular prisms. We must be careful not to double-count any area that is shared between the two prisms. 1. The large, vertical front face is 16 in. by 16 in., so its area is \(16\ in \times 16\ in = 256\ in^2\). 2. The top face of the larger prism is 16 in. by 8 in., so its area is \(16\ in \times 8\ in = 128\ in^2\). 3. The back face of the larger prism, which is identical to the front, is also \(16\ in \times 16\ in = 256\ in^2\). 4. The bottom face of the larger prism is identical to the top face and has an area of \(16\ in \times 8\ in = 128\ in^2\). 5. The left face of the large prism is 16 in. by 8 in., giving an area of \(16\ in \times 8\ in = 128\ in^2\). Now let's consider the smaller, attached prism: 6. The visible part of the right side of the larger prism is an 8 in. by 8 in. square (above the smaller prism), with an area of \(8\ in \times 8\ in = 64\ in^2\). 7. The front face of the smaller prism is 6 in. by 8 in., giving an area of \(6\ in \times 8\ in = 48\ in^2\). 8. The top face of the smaller prism (visible portion) is 6 in. by 8 in., with an area of \(6\ in \times 8\ in = 48\ in^2\). 9. The right-side face of the smaller prism (aligned with the front face of the larger prism) is 6 in. by 16 in., with an area of \(6\ in \times 16\ in = 96\ in^2\). Now let's add up all these areas to find the total surface area: \(256\ in^2 + 128\ in^2 + 256\ in^2 + 128\ in^2 + 128\ in^2 + 64\ in^2 + 48\ in^2 + 48\ in^2 + 96\ in^2 = 1152\ in^2\). So the total surface area of the figure is 1,152 square inches.

Calculating Volume of Composite 3D Figure

To find the volume of the composite figure in the image, consider it as two separate rectangular prisms and then add their volumes together. **First rectangular prism:** The dimensions of the larger prism include the entire length, width, and height of the figure. - Length (l₁) = 9.1 cm - Width (w₁) = 2.4 cm + 4.7 cm + 2.4 cm - Height (h₁) = 2.4 cm Calculate the volume (V₁) of the first prism: V₁ = l₁ × w₁ × h₁ V₁ = 9.1 cm × (2.4 cm + 4.7 cm + 2.4 cm) × 2.4 cm V₁ = 9.1 cm × 9.5 cm × 2.4 cm V₁ = 9.1 cm × 22.8 cm V₁ = 207.48 cm³ **Second rectangular prism (the cut-out section):** The dimensions of the cut-out are given inside the larger prism. - Length (l₂) = 4.7 cm - Width (w₂) = 2.4 cm - Height (h₂) = 2.4 cm Calculate the volume (V₂) of the cut-out section: V₂ = l₂ × w₂ × h₂ V₂ = 4.7 cm × 2.4 cm × 2.4 cm V₂ = 11.328 cm³ Now subtract V₂ from V₁ to get the total volume (V) of the composite figure: V = V₁ - V₂ V = 207.48 cm³ - 11.328 cm³ V ≈ 196.152 cm³ Round to the nearest hundredth, if necessary: V ≈ 196.15 cm³ So, the volume of the composite figure is approximately 196.15 cubic centimeters.

Determining Planes Containing Line Segment DH in a 3D Figure

The image shows a question that asks for two different planes that contain the line segment DH in a three-dimensional figure, which is described as a rectangular shipping box. Without the actual visual of the figure, I cannot determine the exact position of the line segment DH or identify the planes it lies on. However, based on typical conventions for naming points in a rectangular prism or box, DH would likely be a line segment on one of the edges of the box. To answer a question like this, one would generally look for two planes that share this line segment. For example, if D and H were opposite corners on the top surface of the box, then plane ADH (including one adjacent side) and plane HDG (including the other adjacent side) would contain DH. This is just a general description and can't be confirmed without seeing the specific figure. Given the choice options: A) Plane ADE, Plane CGH B) Plane ADE, Plane FBC C) Plane ADC, Plane CGH D) Plane FBC, Plane ADC Without the figure, these choices do not provide enough context to determine which two planes contain DH. Please provide the visual of the box, or additional information so I can help you determine the correct answer.

Geometry Problem: Calculating Height of a Rectangular Prism

Dựa trên hình ảnh bạn cung cấp, đây là một bài toán hình học liên quan đến hình hợp. Theo thông tin được đề cập, hình hợp này có chiều dài là 4,5dm, chiều rộng 2,6dm và thể tích của hình hợp là 17,4dm³. Bài toán yêu cầu tính chiều cao của hình hợp đó. Để tính chiều cao của hình hợp, chúng ta sử dụng công thức tính thể tích: Thể tích hình hợp = Chiều dài x Chiều rộng x Chiều cao Mặc định, thể tích của hình hợp đã được cung cấp trong đề bài. Ta cần tìm chiều cao, vì vậy ta sẽ biến đổi công thức để chiều cao là phần tử cần tìm: Chiều cao = Thể tích hình hợp / (Chiều dài x Chiều rộng) Thay số liệu cụ thể vào công thức, ta có: Chiều cao = 17,4dm³ / (4,5dm x 2,6dm) Chiều cao = 17,4 / 11,7 Chiều cao ≈ 1,49dm Vậy chiều cao của hình hợp là khoảng 1,49dm.

Calculating the Volume of a Rectangular Prism

The image displays a rectangular prism (also known as a rectangular solid or a cuboid) with labeled dimensions. The dimensions given are 13 cm for the length, 5 cm for the width (or depth), and 6 cm for the height. If the question from the image is to find the volume of the rectangular prism, the formula to use is: Volume = length × width × height Applying the given dimensions to this formula: Volume = 13 cm × 5 cm × 6 cm Volume = 65 cm² × 6 cm Volume = 390 cm³ The volume of the rectangular prism is 390 cubic centimeters.

Calculating the Volume of a Rectangular Prism

The image depicts a rectangular prism, where the dimensions are given as follows: - Length (l): \( 16\frac{1}{2} \) cm or 16.5 cm - Width (w): 4 cm - Height (h): \( 9\frac{3}{4} \) cm or 9.75 cm Assuming you are looking to calculate the volume of this rectangular prism, the formula to use is: \[ \text{Volume} = l \times w \times h \] Let's insert the given values: \[ \text{Volume} = 16.5 \text{ cm} \times 4 \text{ cm} \times 9.75 \text{ cm} \] Now calculate each multiplication step by step: \[ \text{Volume} = 66 \text{ cm}^2 \times 9.75 \text{ cm} \] \[ \text{Volume} = 643.5 \text{ cm}^3 \] So, the volume of the given rectangular prism is 643.5 cubic centimeters.

Calculating Volume of a Rectangular Prism

The volume of a rectangular prism (which is the shape shown in the image) is calculated by multiplying its length, width, and height. From the image, the length is given as 9 mm, the width as 8 mm, and the height as 2 mm. Volume = length × width × height Volume = 9 mm × 8 mm × 2 mm Volume = 72 mm² × 2 mm Volume = 144 mm³ So the volume of the prism is 144 cubic millimeters.

Calculating the Volume of a Composite Solid

To find the volume of this composite solid, we need to break it into smaller parts whose volumes we can calculate easily and then sum up those volumes. By looking at the shapes, we can split the figure into two rectangular prisms. Let's call the one on the left "Prism A" and the one on the right "Prism B". 1. **Volume of Prism A**: For Prism A, we have the dimensions 2 cm by 6 cm by 10 cm. The volume (V) of a rectangular prism can be found using the formula V = length × width × height. Therefore, V of Prism A = 2 cm × 6 cm × 10 cm = 120 cm³. 2. **Volume of Prism B**: For Prism B, the dimensions are not as straightforward, so we need to calculate the missing dimensions first. We can see that the height of the prism is 5 cm. The length of the prism B can be determined by subtracting the length of prism A from the total length. That is 10 cm (total length) - 6 cm (length of A) = 4 cm. So, the length of prism B is 4 cm. The width of prism B is the total width, which is 8 cm. Therefore, V of Prism B = 5 cm × 4 cm × 8 cm = 160 cm³. Now, we add the volumes of the two prisms together: Total Volume = Volume of Prism A + Volume of Prism B Total Volume = 120 cm³ + 160 cm³ = 280 cm³. The volume of the composite solid is 280 cm³.