3
8
5
5 units wide
8 units long
3 units high
3
8
5
5 units wide
8 units long
3 units high
Back
Top
3
Left
8
Right
5
Front
Bottom
5 units wide
8 units long
3 units high
Top and bottom
Each rectangle is 5 units by 8 units for a total
of 40 square units. The top and the bottom
together have an area of 80 square units.
Front and back
Each rectangle is 3 units by 5 units for a total
of 15 square units. The front and the back
together have an area of 30 square units.
Left and right sides
Each rectangle is 3 units by 8 units for a total
of 24 square units. The left and the right sides
together have an area of 48 square units.
3
8
5
3
8
5
Total area for top and bottom: 80 sq. units
3
8
5
Total area for top and bottom: 80 sq. units
Total area for front and back: 30 sq. units
3
8
5
Total area for top and bottom: 80 sq. units
Total area for front and back: 30 sq. units
Total area for left and right sides: 48 sq. units
3
8
5
Total area for top and bottom: 80 sq. units
Total area for front and back: 30 sq. units
Total area for left and right sides: 48 sq. units
Total surface area for entire box:
80 + 30 + 48 = 158 sq. units.
3
8
5
5 units wide
8 units long
3 units high
3
8
5=w
5 units wide
8 units long
3 units high
3
8=l
5=w
5 units wide
8 units long
3 units high
3=h
8=l
5=w
5 units wide
8 units long
3 units high
3=h
8=l
5=w
lw = area of top and area of bottom.
3=h
8=l
5=w
lw = area of top and area of bottom.
hw = area of front and area of back.
3=h
8=l
5=w
lw = area of top and area of bottom.
hw = area of front and area of back.
lh = area of left side and area of right side.
3=h
8=l
5=w
lw = area of top and area of bottom.
hw = area of front and area of back.
lh = area of left side and area of right side.
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh
3=h
8=l
5=w
lw = area of top and area of bottom.
hw = area of front and area of back.
lh = area of left side and area of right side.
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
back
left
top
front
bottom
right
8
back
left
top
front
bottom
8
right
8
back
5
left
top
right
front
5
bottom
8
5
5
8
5
3
back
left
top
3
front
3
5
bottom
5
8
3
right
5
8
3
5
left
3
5
back
40
top
front
40
bottom
8
3
right
3
5
5
8
3
5
left
3
5
back
24 3
40
top
front 24
40
bottom
8
right
3
5
5
8
3
5
left
15
3
5
back
24 3
40
top
right
15
front 24 3
40
bottom
8
5
5
8
3
5
left
15
3
5
back
24 3
40
top
right
15
front 24 3
40
bottom
8
5
5
24 + 15 + 40 + 15 + 24 + 40
= 158 sq. units
3=h
8=l
5=w
3=h
8=l
5=w
3=h
8=l
5=w
The top layer contains 5 • 8 or 40 cubes. Each
cube is 1 cubic unit.
3=h
8=l
5=w
The top layer contains 5 • 8 or 40 cubes. Each
cube is 1 cubic unit. Since there are 3 layers, we
can do 3 • 40 to get that there are 120 cubes or
120 cubic units in this box.
3=h
8=l
5=w
The top layer contains 5 • 8 or 40 cubes. Each
cube is 1 cubic unit. Since there are 3 layers, we
can do 3 • 40 to get that there are 120 cubes or
120 cubic units in this box. We say the volume
of the box is 120 cubic units.
3=h
8=l
5=w
We multiplied the length times the width (lw) to
get the volume of the top layer.
3=h
8=l
5=w
We multiplied the length times the width (lw) to
get the volume of the top layer.
Then we multiplied that product by the height
(lwh) to get the total volume.
3=h
8=l
5=w
We multiplied the length times the width (lw) to
get the volume of the top layer.
Then we multiplied that product by the height
(lwh) to get the total volume.
Formula for volume:
V = lwh
h = 3.5 in.
w = 4.5 in.
l = 9 in.
h = 3.5 in.
w = 4.5 in.
l = 9 in.
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
h = 3.5 in.
w = 4.5 in.
l = 9 in.
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
S.A. = 2(9 • 4.5 + 3.5 • 4.5 + 9 • 3.5)
h = 3.5 in.
w = 4.5 in.
l = 9 in.
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
S.A. = 2(9 • 4.5 + 3.5 • 4.5 + 9 • 3.5)
S.A. = 2(40.5 + 15.75 + 31.5)
h = 3.5 in.
w = 4.5 in.
l = 9 in.
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
S.A. = 2(9 • 4.5 + 3.5 • 4.5 + 9 • 3.5)
S.A. = 2(40.5 + 15.75 + 31.5)
S.A. = 2(87.5)
h = 3.5 in.
w = 4.5 in.
l = 9 in.
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
S.A. = 2(9 • 4.5 + 3.5 • 4.5 + 9 • 3.5)
S.A. = 2(40.5 + 15.75 + 31.5)
2
S.A. = 2(87.5) =
175.5 in.
h = 3.5 in.
w = 4.5 in.
l = 9 in.
h = 3.5 in.
w = 4.5 in.
l = 9 in.
Formula for volume:
V = lwh
h = 3.5 in.
w = 4.5 in.
l = 9 in.
Formula for volume:
V = lwh
V = 9 • 4.5 • 3.5
h = 3.5 in.
w = 4.5 in.
l = 9 in.
Formula for volume:
V = lwh
V = 9 • 4.5 • 3.5
V = 141.75 in.3
4 cm
2 cm
2 cm
4
4 cm
8
8
2 cm 4
2 cm
8
8
4 cm
2 cm
2 cm
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
4 cm
2 cm
2 cm
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
S.A. = 2(4 • 2 + 2 • 2 + 4 • 2)
4 cm
2 cm
2 cm
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
S.A. = 2(4 • 2 + 2 • 2 + 4 • 2)
S.A. = 2(8 + 4 + 8)
4 cm
2 cm
2 cm
Formula for total surface area:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
S.A. = 2(4 • 2 + 2 • 2 + 4 • 2)
S.A. = 2(8 + 4 + 8)
2
S.A. = 2(20) =
40 cm
4 cm
2 cm
2 cm
Formula for volume:
V = lwh
4 cm
2 cm
2 cm
Formula for volume:
V = lwh
V=4•2•2
4 cm
2 cm
2 cm
Formula for volume:
V = lwh
V=4•2•2
3
V = 16 cm
In this lesson we looked at two
formulas for rectangular solids.
Formula for total surface area of a
rectangular solid:
S.A. = 2lw + 2hw + 2lh or 2(lw + hw + lh)
Formula for volume of a rectangular solid:
V = lwh