Rectangular Prism
Author: Lewis Prisco

Use this worksheet to practice finding the Volume and Surface Area of a Rectangular Prism.  Adjust the height, length, and width using the labeled sliders.  Answer the questions below.  The multi-colored switches can be used to check your work.

1.Find the volume and surface area for 5 different Rectangular Prisms by randomly choosing different heights, lengths and widths.

2. Find the missing dimesion. Round to the nearest unit.
a. Rectangular Prism: volume 450cu ft, height ___, length 7ft, width 6ft

b. Rectangular Prism: surface area 235sq in, height 4.5in, length 7in, width ___

3. Firewood: Wood for a fireplace is often sold by the cord.  A cord is 8ft by 4ft by 4ft.  How many cubic feet are in a cord of wood?

l

w

h

Volume=(h)(l)(w)

Surface Area=2(lw)+2(hw)+2(lh)

Formula for Volume

Solution for Volume

Formula for Surface Area

Solution for Surface Area

height = 10 (slider from 1 to 10, step 0.1)
A = (-4, -2)
E = (14, 5)
F = (14, 6)
G = Dilate(F, height, E)
u = Vector(E, G)
H = (14, 3)
I = (15, 3)
J = (16, 5)
length = 10 (slider from 1 to 10, step 0.1)
width = 10 (slider from 1 to 10, step 0.1)
L = Dilate(I, length, H)
v = Vector(H, L)
g = Circle(J, width)
K = (15.033333333333333, 4.7)
h = Line(J, K)
M = Intersect(g, h, 1.0)
w = Vector(J, M)
B = Translate(A, v)
d = Circle(J, 1.0)
C = Translate(A, Vector[w / 2.0])
D = Translate(C, v)
P, a, c, d_1, b = Polygon(A, C, D, B)
A' = Translate(A, u)
C' = Translate(C, u)
D' = Translate(D, u)
B' = Translate(B, u)
P', a', c', d', b' = Polygon(A', C', D', B')
Q, a'_1, a_1, c_1, c'_1 = Polygon(A', A, C, C')
R, c'_2, d'_1, d_2, c_2 = Polygon(C', D', D, C)
S_1, a'_2, a_2, b_1, b'_1 = Polygon(A', A, B, B')
T, b'_2, d'_2, d_3, b_2 = Polygon(B', D', D, B)
N = Midpoint(A', A)
O = Midpoint(B, A)
U = Midpoint(D, B)
VolumeFormula = 0 (slider from 0 to 1, step 1)
SurfaceAreaFormula = 0 (slider from 0 to 1, step 1)
V_1 = (15.233333333333333, 9)
W = (15, 5)
Y = If(VolumeFormula ≟ 1.0, V_1)
Z = If(SurfaceAreaFormula ≟ 1.0, W)
v_1: height * length * width
A_1 = (15.066666666666666, 7.166666666666667)
T6: v_1 + " =(" + height + ")(" + length + ")(" + width + ")"
C_1 = (14.866666666666667, 3.8666666666666667)
D_1 = If(SurfaceAreaFormula ≟ 1.0, C_1)
s_2: 2.0 * length * width + 2.0 * height * width + 2.0 * length * height
T8: s_2 + "=" + "2(" + length + ")(" + width + ")+2(" + height + ")(" + width + ")+2(" + length + ")(" + height + ")"
VolumeSolution = 1 (slider from 0 to 1, step 1)
SurfaceAreaSolution = 0 (slider from 0 to 1, step 1)
S = If(VolumeSolution ≟ 1.0, A_1)
B_1 = If(SurfaceAreaSolution ≟ 1.0, C_1)
T4: "height=" + height
T9: "length=" + length
T10: "width=" + width