Volume and surface area formulae

1. Beaconhouse School System SBGR

2D –geometric shape: square, rectangle, triangle, circle, trapezoid, parallelogram, etc.




Composite figure: a combination of 2 or more geometric shapes e.g. e.g.


3D –geometric shape: rectangular prism, triangular prism, cylinder, cone, sphere, pyramid, etc.





Calculate the Perimeter of a Rectangle: distance around the rectangle (add up the lengths of all 4 sides)

P = L + L + W + W or P = 2L + 2W or P = 2(L + W)




Calculate the Area of a Rectangle: number of square units that it covers (multiply length x width)

A = L x W

Calculate the Perimeter of a Square: distance around the square (add up length of all 4 sides)

P = L + L + L + L or P = 4L



Calculate the Area of a Square: number of square units that it covers (multiply length x length)

A = L x L or A = L
2



Calculate the Perimeter of a Triangle: distance around the triangle (add up the lengths of all 3 sides)

P = a + b + c



Calculate the Area of a Triangle: number of square units that it covers ( ½ x base of triangle x height of triangle)

A = 2
height x base A = 2
h b


Calculate the Circumference of a Circle: distance around the circle (the “perimeter” of the circle)

C = 2 r or C = d
(r is radius) (d is diameter)



Calculate the Area of a Circle: number of square units that it covers ( x radius x radius)

A = r
2
A = x r x r

Calculate the Surface Area of a Rectangular Prism: add up the areas of all 6 sides of the prism
SA = (2 x L x W) + (2 x L x H) + (2 x W x H)
Or SA = 2(LW + LH + WH)




Calculate the Volume of a Rectangular Prism: amount of space it takes up (area of base x height of prism)

V = area of the rectangle base x height of the prism
V = L x W x H

c
b
a
r d
L
W
H
L
W
H
b
h h
b
L
W
L
W
L
L
L
L

2. Beaconhouse School System SBGR

Calculate the Surface Area of a Triangular Prism: add up the area of all 5 sides (2 triangles, 3 rectangles) of the prism

SA = 2
height x base + 2
height x base + LW + LW + LW

SA = area triangle + area triangle + area rectangle + area rectangle + area rectangle



Calculate the Volume of a Triangular Prism: amount of space it takes up (area of base triangle x height of prism)

V = area of base triangle x height of prism
V = 2
height x base x height of prism V = 2
bh x h of prism



Calculate the Surface Area of a Cylinder: area of the 2 circles and the area of the rectangle

SA = 2 r
2
+ 2 r x height of cylinder
SA = ( area of 2 circles 2 r
2
) + ( area of rectangle 2 r x h )



Calculate the Volume of a Cylinder: amount of space it takes up

V = r
2
x h
V = (area of the base circle r
2
) x ( height of the cylinder h )


Calculate the Volume of a Cone: amount of space it takes up
V = 3
1 r
2
x h OR V = 3
hr
2
V = (1/3) x (area of the base circle) x (height of the cone)




Calculate the Surface Area of a Sphere: amount of space it takes up

SA = 4 r
2

SA = 4 x area of the circle cross-section ( r
2
) at the equator of the sphere



Calculate the Volume of a Sphere: amount of space it takes up

V = 3
r
3
4



Calculate the Surface Area of a Square-Based Pyramid: area of all the faces (square base, and 4 triangles)

SA = b
2
+ 4(2
h b ) where s = (slant) height of a triangular face
SA = (area of the square base + areas of 4 side triangles)



Calculate the Volume of a Square-Based Pyramid: amount of space it takes up

V = hb
3
1
2
V = one-third the area of the square base (b
2
) x height of the pyramid (h)
height of prism
h
b
r
h
r
h
r
h
r
r
b
b
s
b
b
h