Volume of Prisms and Cylinders
Table Of Contents
🎬 Math Angel Video: Volume of a Prism and a Cylinder
Prism and Cylinder Volume Formula
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The volume of a prism or cylinder is calculated using the formula:
$$ V = B \times h $$
where $B$ is the area of the base and $h$ is the height.
- For a cylinder, the base is a circle, so its area is:
$$ B = \pi r^2 $$
Thus, the volume of a cylinder is:
$$ V = \pi r^2\times h $$
How to Calculate Volume of a Prism (Example)
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Here, the base is a triangle, so we calculate its area using:
$$ B = \frac{1}{2} \times \text{base} \times \text{height} $$
$$ B = \frac{1}{2} \times 4 \text{ cm} \times 3 \text{ cm} = 6 \text{ cm}^2 $$
Now, multiply by the height, the volume of the prism is:
$$ V = B \times h = 6 \text{ cm}^2 \times 5 \text{ cm} = 30 \text{ cm}^3 $$
Thus, the volume of this prism is $30 \text{ cm}^3 $.
How to Calculate Volume of a Cylinder (Application)
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Here, the base of this can is a circle with radius $r = 2$ cm, so its area is:
$$ B = \pi r^2 = \pi \times (2 \text{ cm})^2 = 4\pi \text{ cm}^2 $$
Given that $h = 5$ cm, the volume of the cylinder is:
$$ V = B \times h = 4\pi \text{ cm}^2 \times 5 \text{ cm} = 20\pi \text{ cm}^3 $$
Approximating $\pi \approx 3.14$:
$$ V \approx 20 \times 3.14 \approx 62.8 \text{ cm}^3 $$
Thus, the volume of this cylinder is around $ 62.8 \text{ cm}^3 $.
🍪 Quiz: Practice Finding Volume of Prisms or Cylinders
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