# Right Rectangular Prism

Right Rectangular Prism = Three-Dimensional Shape in which Opposite Faces are Equal (with all right angles)

Basics

l = length
w = width
h = height
p = perimeter of base
B = area of base
Base = floor of prism
SA = Surface Area = area covering all surfaces of prism (measured in square units)
V = Volume = space occupied by prism (measured in cubic units)

A cube is a special version of a right rectangular prism in which all faces are equal.

Formulas (Mathematics Formula Sheet)

SA = ph + 2B
V = Bh

Formulas (NOT on Mathematics Formula Sheet)

p = 2l + 2w
B = lw
h = V ÷ B

Question
A cinder block has a length of 100 centimeters, width 60 centimeters, and height 80 centimeters.  What is its surface area?

37600 square centimeters

p = 2l + 2w
p = 2 × 100 + 2 × 60 = 320

B = lw
B = 100 × 60 = 6000

SA = ph + 2B
SA = 320 × 80 + 2 × 6000 = 37600

Input Display Comment
2 × 100 + 2 × 60 2*100+2*60 p = 2l + 2w
320 p
100 × 60 100*60 B = lw
6000 B
320 × 80 + 2 × 6000 320*80+2*6000 SA = ph + 2B
###### Right Rectangular Prism

Question
With reference to the question above, what is the cinder block’s surface area in square meters?

3.76 square meters

See Measurement.
Square Meters = Square Centimeters ÷ 10000 square centimeters per square meter
Square Meters = 37600 ÷ 10000 = 3.76 square meters

Input Display Comment
2 × 100 + 2 × 60 2*100+2*60 p = 2l + 2w
320 p
100 × 60 100*60 B = lw
6000 B
320 × 80 + 2 × 6000 320*80+2*6000 SA = ph + 2B
37600
37600 ÷ 10000 37600÷10000 Square Meters = Square Centimeters ÷ 10000 square centimeters per square meter
###### Right Rectangular Prism

Question
A cinder block has a length of 100 centimeters, width 60 centimeters, and height 80 centimeters.  What is its volume?

480000 cubic centimeters

B = lw
B = 100 × 60 = 6000

V = Bh
V = 6000 × 80 = 480000

Input Display Comment
100 × 60 100*60 B = lw
6000 B
6000 × 80 6000*80 V = Bh
###### Right Rectangular Prism

Question
With reference to the question above, what is the cinder block’s volume in cubic meters?

0.48 cubic meters

See Measurement.
Cubic Meters = Cubic Centimeters ÷ 1000000 cubic centimeters per cubic meter
Cubic Meters =
480000 ÷ 1000000 = 0.48 cubic meters

Input Display Comment
100 × 60 100*60 B = lw
6000 B
6000 × 80 6000*80 V = Bh
480000
480000 ÷ 1000000 480000÷1000000 Cubic Meters = Cubic Centimeters ÷ 1000000 cubic centimeters per cubic meter
###### Right Rectangular Prism

Question
A toy block has a length of $\bf\displaystyle10\frac{1}{2}$ centimeters, width $\bf\displaystyle6\frac{1}{2}$ centimeters, and height $\bf\displaystyle8\frac{1}{2}$ centimeters.  To the nearest hundredth of a cubic centimeter, what is its volume?

580.13 cubic centimeters

B = lw

B = $\bf\displaystyle10\frac{1}{2}\times 6\frac{1}{2}$ = $\bf\displaystyle\frac{273}{4}$

V = Bh

V = $\bf\displaystyle\frac{273}{4}\times 8\frac{1}{2}$ = $\bf\displaystyle\frac{4641}{8}$ = 580.125 after toggle = 580.13 after rounding

Input Display Comment
10  1  2
×

6  1  2
$\bf\displaystyle10\frac{1}{2}*6\frac{1}{2}$ B = lw
$\bf\displaystyle\frac{273}{4}$ B
273  4
×

8  1  2
$\bf\displaystyle\frac{273}{4}*8\frac{1}{2}$ V = Bh
$\bf\displaystyle\frac{4641}{8}$
(before rounding)
###### Right Rectangular Prism

Question
A cinder block has a length of 120 centimeters, width 50 centimeters, and volume 780000 cubic centimeters.  What is its height?

130 centimeters

B = lw
B = 120 × 50 = 6000

h = V ÷ B
h = 780000 ÷ 6000 = 130

Input Display Comment
120 × 50 120*50 B = lw
6000 B
780000 ÷ 6000 h = V ÷ B
###### Right Rectangular Prism

Practice – Questions
1.  A cinder block has a length of 50 centimeters, width 30 centimeters, and height 40 centimeters.  What is its surface area?

2.  With reference to Question 1, what is the cinder block’s surface area in square meters?

3.  A cinder block has a length of 50 centimeters, width 30 centimeters, and height 40 centimeters.  What is its volume?

4.  A toy block has a length of $\bf\displaystyle5\frac{1}{2}$ centimeters, width $\bf\displaystyle3\frac{1}{2}$ centimeters, and height $\bf\displaystyle4\frac{1}{2}$ centimeters.  To the nearest hundredth of a cubic centimeter, what is its volume?

5.  A cinder block has a length of 60 centimeters, width 25 centimeters, and volume 67500 cubic centimeters.  What is its height?