Volumes of Solids
Aligned to G-GMD.A.3 — Common Core State Standards for Mathematics.
What this lesson teaches
Volume formulas: cylinder = pi*r^2*h; cone = (1/3)*pi*r^2*h; pyramid = (1/3)*base area*height; sphere = (4/3)*pi*r^3. The cone and pyramid each hold one-third of the prism or cylinder with the same base and height.
Worked example
Find the volume of a cone with radius 3 and height 10. Use V = (1/3)*pi*r^2*h. Substitute: V = (1/3)*pi*(3)^2*(10) = (1/3)*pi*9*10 = (1/3)*90*pi = 30*pi. Numerically that is about 94.2 cubic units. Note this is exactly one-third of a cylinder with the same base and height (90*pi).
Practice questions
- Find the volume of a cylinder with radius 4 and height 7.
- Find the volume of a sphere with radius 6.
- A pyramid has a square base of side 5 and height 12. Find its volume.
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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
Volúmenes de sólidos
Fórmulas de volumen: cilindro = pi*r^2*h; cono = (1/3)*pi*r^2*h; pirámide = (1/3)*área de la base*altura; esfera = (4/3)*pi*r^3. El cono y la pirámide contienen cada uno un tercio del prisma o cilindro con la misma base y altura.
Ejemplo: Halla el volumen de un cono con radio 3 y altura 10. Usa V = (1/3)*pi*r^2*h. Sustituye: V = (1/3)*pi*(3)^2*(10) = (1/3)*pi*9*10 = (1/3)*90*pi = 30*pi. Numéricamente es unos 94.2 unidades cúbicas. Nota que es exactamente un tercio de un cilindro con la misma base y altura (90*pi).
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