Math Problem Statement
Solution
The shape in the diagram consists of two distinct parts: a rectangular prism (cuboid) on top and a cylinder on the bottom. Let's calculate the volume of each part separately, and then sum them to get the total volume.
1. Volume of the Rectangular Prism (Cuboid)
The volume of a cuboid is calculated by:
From the diagram, the cuboid's dimensions are:
- Length = 5 cm
- Width = 5 cm
- Height = 10 cm
So, the volume of the cuboid is:
2. Volume of the Cylinder
The volume of a cylinder is calculated by:
From the diagram, the cylinder's dimensions are:
- Radius = 4 cm / 2 = 2 cm
- Height = 8 cm
So, the volume of the cylinder is:
Using :
3. Total Volume
Now, we sum the volumes of the cuboid and the cylinder:
Thus, the total volume of the shape is approximately 350.53 cm³.
Do you have any questions, or would you like more details? Here are some related questions to explore:
- How would the total volume change if the radius of the cylinder was increased?
- What formula would you use to calculate the surface area of this combined shape?
- How would the volume change if the height of the cuboid was doubled?
- Can you calculate the total volume if the cylinder height was halved but the radius was doubled?
- How does the value of affect the accuracy of volume calculations for the cylinder?
Tip: Always keep track of units when calculating volumes to avoid confusion, especially when mixing different shapes.
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume Calculation
3D Shapes
Formulas
V_cuboid = length × width × height
V_cylinder = π × r^2 × height
Theorems
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Suitable Grade Level
Grades 8-10
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