Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
KEYS
h = height
s = slant height
a = side length
e = lateral edge length
r = a/2
V = volume
Stot = total surface area
Slat = lateral surface area
Sbot = bottom surface area
Surface Area Formulas:
Capsule Surface Area
Volume = πr2((4/3)r + a)
Surface Area = 2πr(2r + a)
Circular Cone Surface Area
Volume = (1/3)πr2h
Lateral Surface Area = πrs = πr√(r2 + h2)
Base Surface Area = πr2
Total Surface Area
= L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))
Circular Cylinder Surface Area
Volume = πr2h
Top Surface Area = πr2
Bottom Surface Area = πr2
Total Surface Area
= L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
Conical Frustum Surface Area
Volume = (1/3)πh (r12 + r22 + (r1 * r2))
Lateral Surface Area
= π(r1 + r2)s = π(r1 + r2)√((r1 - r2)2 + h2)
Top Surface Area = πr12
Base Surface Area = πr22
Total Surface Area
= π(r12 + r22 + (r1 * r2) * s)
= π[ r12 + r22 + (r1 * r2) * √((r1 - r2)2 + h2) ]
Cube Surface Area
Volume = a3
Surface Area = 6a2
Hemisphere Surface Area
Volume = (2/3)πr3
Curved Surface Area = 2πr2
Base Surface Area = πr2
Total Surface Area= (2πr2) + (πr2) = 3πr2
Pyramid Surface Area
Volume = (1/3)a2h
Lateral Surface Area = a√(a2 + 4h2)
Base Surface Area = a2
Total Surface Area
= L + B = a2 + a√(a2 + 4h2))
= a(a + √(a2 + 4h2))
Rectangular Prism Surface Area
Volume = lwh
Surface Area = 2(lw + lh + wh)
Sphere Surface Area
Volume = (4/3)πr3
Surface Area = 4πr2
Spherical Cap Surface Area
Volume = (1/3)πh2(3R - h)
Surface Area = 2πRh
Triangular Prism Surface Area
Top Surface Area of a Triangular Prism Formula
Atop=14(a+b+c)(b+c−a)(c+a−b)(a+b−c)√
Bottom Surface Area of a Triangular Prism Formula
Abot=14(a+b+c)(b+c−a)(c+a−b)(a+b−c)√
Lateral Surface Area of a Triangular Prism Formula
Alat=h(a+b+c)
Total Surface Area of a Triangular Prism Formula
Atot=Atop+Abot+Alat
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