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Listed below are a basic list of the most common volume and surface area formulas for 3 dimensional shapes or solid figures.
VOLUME FORMULA FOR SOLID FIGURES:
| Shape |
Volume |
Surface Area |
Cube
|
Volume = S x S x S |
S. Area = 6 x S x S |
Rectangular Prism
|
Volume = L x W x H |
S. Area = 2 (L x W) + 2(Lx H) + 2(W x H) |
Cylinder
|
Volume = B x H
where: B =  r2 |
S. Area = (C x H) + 2 (2 x B)
where: C = x D |
Cone
|
Volume = (B x VH) / 3
where: B = r2 |
S. Area = ( C x SH ) / 2 + B
where: C = x D |
Frustum of Cone
|
Volume = (VH / 3) x (r2 + R2 +  B x b ) |
S. Area = x SH x (r + R) + b + B
where B = area of base, b = area on top, R = radius at base, r = radius at top, SH = slope height |
Pyramid
|
Volume = (B x VH) / 3 |
S. Area = (P x SH) / 2 + B
where: B = area of base, P = perimeter of base, SH = slope height |
Frustum of Pyramid
|
Volume = (B + b + ((B x b)) x VH) /3 |
S. Area = (SH / 2) x (p + P) + B + b |
Sphere
|
Volume = 0.5236 x D x D x D
Note: / 6 = 0.5236 |
S. Area = x D x D
|
Zone of Sphere
|
Volume: ( x H)/6 x ((3 x R x R) + (3 x r x r) + (H x H))
where: R = radius at base, r = radius at top |
S. Area = x D x H (excluding base & top) |
Segment of Sphere
|
Volume = ( x H x H)/3 x (3R - H)
where: R = radius of sphere |
S. Area = x D x H (excluding base) |
Wedge
|
Volume = (W x H x S) / 3 |
S. Area = S ((H x H) + (W x W)) + (H x S) + (H x W) + (S x W) |
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