Modeling Objects with Shapes
Aligned to G-MG.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
Real objects can be approximated by geometric shapes so their measurements can be computed. A can is a cylinder, a tent may be a triangular prism, a scoop of ice cream a sphere. Choosing a close shape lets you estimate area, volume, or capacity.
Worked example
Model a grain silo as a cylinder to estimate its capacity. A silo is 4 m across and 10 m tall, so radius = 2 m. Volume = pi*r^2*h = pi*(2)^2*(10) = pi*4*10 = 40*pi cubic meters, about 125.7 cubic meters. This models the storage capacity even though a real silo has a slightly domed top.
Practice questions
- What geometric solid best models a soup can, and what two measurements do you need for its volume?
- A traffic cone is about 0.2 m in base radius and 0.7 m tall. Estimate its volume as a cone.
- Name a geometric shape that models a basketball and give the formula for its volume.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Modelar objetos con formas
Los objetos reales se pueden aproximar con formas geométricas para calcular sus medidas. Una lata es un cilindro, una tienda de campaña puede ser un prisma triangular, una bola de helado una esfera. Elegir una forma cercana permite estimar área, volumen o capacidad.
Ejemplo: Modela un silo de grano como cilindro para estimar su capacidad. Un silo mide 4 m de ancho y 10 m de alto, así que el radio = 2 m. Volumen = pi*r^2*h = pi*(2)^2*(10) = pi*4*10 = 40*pi metros cúbicos, unos 125.7 metros cúbicos. Esto modela la capacidad de almacenamiento aunque un silo real tenga una tapa algo abovedada.
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