Math Problem Statement

The original question is based on the provided image showing two rectangular prisms, asking for the measures of sides A, B, and C, and the volumes of the two figures, along with the total volume.

Solution

Let's break down the information provided in the image and solve the problem step by step.

Given:

  • Figure 1: A rectangular prism with dimensions:

    • Length: 2cm2 \, \text{cm}
    • Width: 3cm3 \, \text{cm}
    • Height: 5cm5 \, \text{cm}
  • Figure 2: A second rectangular prism with dimensions:

    • Length: 8cm8 \, \text{cm}
    • Width: 3cm3 \, \text{cm}
    • Height: 3cm3 \, \text{cm}

Step 1: Measures of sides A, B, C

From the diagram:

  • Side A: This is the length of Figure 2. From the diagram, Side A = 8 cm.
  • Side B: This is the height of Figure 2, which is 3 cm.
  • Side C: This is the width of Figure 1, which is 2 cm.

Step 2: Volume calculations

The volume VV of a rectangular prism is given by the formula: V=Length×Width×HeightV = \text{Length} \times \text{Width} \times \text{Height}

  1. Volume of Figure 1: V1=2cm×3cm×5cm=30cm3V_1 = 2 \, \text{cm} \times 3 \, \text{cm} \times 5 \, \text{cm} = 30 \, \text{cm}^3

  2. Volume of Figure 2: V2=8cm×3cm×3cm=72cm3V_2 = 8 \, \text{cm} \times 3 \, \text{cm} \times 3 \, \text{cm} = 72 \, \text{cm}^3

Step 3: Total volume

The total volume is the sum of the volumes of the two figures: Vtotal=V1+V2=30cm3+72cm3=102cm3V_{\text{total}} = V_1 + V_2 = 30 \, \text{cm}^3 + 72 \, \text{cm}^3 = 102 \, \text{cm}^3

Summary of answers:

  • Measure of Side A: 8cm8 \, \text{cm}
  • Measure of Side B: 3cm3 \, \text{cm}
  • Measure of Side C: 2cm2 \, \text{cm}
  • Volume of Figure 1: 30cm330 \, \text{cm}^3
  • Volume of Figure 2: 72cm372 \, \text{cm}^3
  • Total Volume: 102cm3102 \, \text{cm}^3

Would you like further details or have any questions?

Related questions:

  1. What would happen if one of the dimensions of Figure 1 doubled?
  2. How would the total volume change if Figure 2’s height increased by 2 cm?
  3. What is the surface area of Figure 1?
  4. How does changing the width of Figure 2 affect its volume?
  5. Can you calculate the diagonal of Figure 1?

Tip:

Always ensure that units are consistent when performing volume calculations to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of Rectangular Prisms

Formulas

Volume = Length × Width × Height

Theorems

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Suitable Grade Level

Grades 4-6