≡Mathematics EN 9th grade: Volume of surface areas of solids
1. Cube
✔ All edges are equal 𝑎
Total surface area:
\( A = 6a^2 \)
Volume:
\( V = a^3 \)
📌 Example:
\( a = 3 \)
\( V = 3^3 = 27 \)
2. Rectangular Prism (Cuboid)
✔ Dimensions: 𝑎, 𝑏, 𝑐
Total surface area:
\( A = 2(ab + ac + bc) \)
Volume:
\( V = abc \)
📌 Example:
\( a = 2, b = 3, c = 4 \)
\( V = 24 \)
3. Triangular Prism
✔ Triangular base
Volume:
\( V = A_{base} \cdot h \)
If the base is a triangle:
\( A_{base} = \frac{b \cdot h}{2} \)
4. Cylinder
✔ Circular base
Total surface area:
\( A = 2\pi r^2 + 2\pi r h \)
Volume:
\( V = \pi r^2 h \)
📌 Example:
\( r = 2, h = 5 \)
\( V = 20\pi \)
5. Cone
✔ Circular base
Volume:
\( V = \frac{1}{3}\pi r^2 h \)
Total surface area:
\( A = \pi r^2 + \pi r g \)
6. Triangular Pyramid
✔ Triangular base
Volume:
\( V = \frac{1}{3} A_{base} \cdot h \)
7. Sphere
✔ Only radius 𝑟
Surface area:
\( A = 4\pi r^2 \)
Volume:
\( V = \frac{4}{3}\pi r^3 \)
📌 Example:
\( r = 3 \)
\( V = \frac{4}{3}\pi \cdot 27 = 36\pi \)
8. Quick Summary
✔ Cube → \( V = a^3 \)
✔ Prism → \( V = A_{base} \cdot h \)
✔ Cylinder → \( V = \pi r^2 h \)
✔ Cone/Pyramid → \( V = \frac{1}{3} A_{base} \cdot h \)
✔ Sphere → \( V = \frac{4}{3}\pi r^3 \)
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