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)

edges

faces

vertices

height = 10 (slider from 1 to 10, step 0.1)
A = (-4, -2)
E_1 = (14, 5)
F_1 = (14, 6)
G_1 = Dilate(F_1, height, E_1)
u = Vector(E_1, G_1)
H_1 = (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_1)
v = Vector(H_1, 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)
E = Translate(A, u)
G = Translate(C, u)
H = Translate(D, u)
F = Translate(B, u)
P', a', c', d', b' = Polygon(E, G, H, F)
Q, a'_1, a_1, c_1, c'_1 = Polygon(E, A, C, G)
R, c'_2, d'_1, d_2, c_2 = Polygon(G, H, D, C)
S_1, a'_2, a_2, b_1, b'_1 = Polygon(E, A, B, F)
T, b'_2, d'_2, d_3, b_2 = Polygon(F, H, D, B)
N = Midpoint(E, A)
O = Midpoint(B, A)
U = Midpoint(D, B)
V_1 = (15.233333333333333, 9)
W = (15, 5)
v_1: height * length * width
A_1 = (15.066666666666666, 7.166666666666667)
T6: v_1 + " =(" + height + ")(" + length + ")(" + width + ")"
C_1 = (14.866666666666667, 3.8666666666666667)
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 + ")"
T4: "height=" + height
T9: "length=" + length
T10: "width=" + width
e = Segment(E, F)
f = Segment(F, H)
i = Segment(H, G)
j = Segment(G, E)
k = false
l = Segment(E, A)
m = Segment(A, B)
n = Segment(B, F)
p = Segment(H, D)
q = Segment(D, B)
r = Segment(D, C)
s = Segment(C, A)
t = Segment(C, G)
poly1, g_1, e_1, f_1, h_1 = Polygon(G, E, F, H)
poly2, e_2, a_3, c_3, g_2 = Polygon(E, A, C, G)
poly3, a_4, b_3, d_4, c_4 = Polygon(A, B, D, C)
poly4, h_2, f_2, b_4, d_5 = Polygon(H, F, B, D)
poly5, h_3, g_3, c_5, d_6 = Polygon(H, G, C, D)
o = false
poly6, e_3, f_3, b_5, a_5 = Polygon(E, F, B, A)
S = Intersect(a, a_1)
V = Intersect(b, a_2)
Z = Intersect(a, a_1)
B_1 = Intersect(b, a)
D_1 = Intersect(d_1, d_3)
I_1 = Intersect(d_1, d_3)
J_1 = Intersect(b, b_2)
K_1 = Intersect(d_1, c)
L_1 = Intersect(c_1, c_2)
M_1 = Intersect(c, a)
N_1 = Intersect(b', a')
O_1 = Intersect(b', d')
P_1 = Intersect(d', c'_2)
Q_1 = Intersect(c', c'_2)
R_1 = Intersect(c', c'_2)
T_1 = Intersect(c'_1, c')
z = false