Right Rectangular Prism

Scott Solomon


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

Right Rectangular Prism


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?

Answer
37600 square centimeters

Answer Process
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
clear blinker clears screen
2 × 100 + 2 × 60 2*100+2*60 p = 2l + 2w
enter 320 p
100 × 60 100*60 B = lw
enter 6000 B
320 × 80 + 2 × 6000 320*80+2*6000 SA = ph + 2B
enter 37600 Answer
Right Rectangular Prism


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

Answer
3.76 square meters

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

Input Display Comment
clear blinker clears screen
2 × 100 + 2 × 60 2*100+2*60 p = 2l + 2w
enter 320 p
100 × 60 100*60 B = lw
enter 6000 B
320 × 80 + 2 × 6000 320*80+2*6000 SA = ph + 2B
enter 37600
37600 ÷ 10000 37600÷10000 Square Meters = Square Centimeters ÷ 10000 square centimeters per square meter
enter  3.76 Answer
Right Rectangular Prism


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

Answer
480000 cubic centimeters

Answer Process
B = lw
B = 100 × 60 = 6000

V = Bh
V = 6000 × 80 = 480000

Input Display Comment
clear blinker clears screen
100 × 60 100*60 B = lw
enter 6000 B
6000 × 80 6000*80 V = Bh
enter 480000 Answer
Right Rectangular Prism


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

Answer
0.48 cubic meters

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

Input Display Comment
clear blinker clears screen
100 × 60 100*60 B = lw
enter 6000 B
6000 × 80 6000*80 V = Bh
enter 480000
480000 ÷ 1000000 480000÷1000000 Cubic Meters = Cubic Centimeters ÷ 1000000 cubic centimeters per cubic meter
enter 0.48 Answer
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?

Answer
580.13 cubic centimeters

Answer Process
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
clear blinker clears screen
2nd mixed number 10 right 1 down 2 right
×
2nd mixed number 6 right 1 down 2 right		 \bf\displaystyle10\frac{1}{2}*6\frac{1}{2} B = lw
enter \bf\displaystyle\frac{273}{4} B
fraction 273 down 4 right
×
2nd mixed number 8 right 1 down 2 right		 \bf\displaystyle\frac{273}{4}*8\frac{1}{2} V = Bh
enter \bf\displaystyle\frac{4641}{8}
toggle 580.125 Answer
(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?

Answer
130 centimeters

Answer Process
B = lw
B = 120 × 50 = 6000

h = V ÷ B
h = 780000 ÷ 6000 = 130

Input Display Comment
clear blinker clears screen
120 × 50 120*50 B = lw
enter 6000 B
780000 ÷ 6000 h = V ÷ B
enter 130 Answer
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?


Practice – Answers
1.  9400 square centimeters

2.  0.94 square meters

3.  60000 cubic centimeters

4.  86.63 cubic centimeters

5.  45 centimeters

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