Surface
Areas
of Prisms and
Cylinders
Use Dimensions of a Solid to Sketch a Solid
Use isometric dot paper to sketch a triangular
prism 6 units high, with bases that are right
triangles with legs 6 units and 4 units long.
Step 1 Mark the corner of the solid, then draw
segments 6 units down, 6 units to the left,
and 4 units to the right.
Use Dimensions of a Solid to Sketch a Solid
Step 2 Draw the triangle for the top of the solid.
Use Dimensions of a Solid to Sketch a Solid
Step 3 Draw segments 6 units down from each
vertex for the vertical edges.
Use Dimensions of a Solid to Sketch a Solid
Step 4 Connect the corresponding vertices. Use
dashed lines for the hidden edges. Shade the
top of the solid.
Answer:
Which diagram shows a rectangular prism 2 units
high, 5 units long, and 2 units wide?
A.
B.
C.
D.
Use an Orthographic Drawing to Sketch a Solid
Use isometric dot paper and the orthographic
drawing to sketch a solid.
•
The top view indicates one row of different heights
and one column in the front right.
Use Dimensions of a Solid to Sketch a Solid
•
The front view indicates that there are four
standing columns. The first column to the left is
2 blocks high, the second column is 3 blocks high,
the third column is 2 blocks high, and the fourth
column to the far right is 1 block high. The dark
segments indicate breaks in the surface.
•
The right view indicates that the front right column
is only 1 block high. The dark segments indicate a
break in the surface.
Use Dimensions of a Solid to Sketch a Solid
•
The left view indicates that the back left column is
2 blocks high.
•
Draw the figure so that the lowest columns are in
front and connect the dots on the isometric dot
paper to represent the edges of the solid.
Answer:
Which diagram is the correct
corner view of the figure given top
the orthographic drawing?
view
A.
B.
C.
D.
left
view
front
view
right
view
Identify Cross Sections of Solids
BAKERY A customer ordered a two-layer sheet
cake. Determine the shape of each cross section
of the cake below.
Identify Cross Sections of Solids
Answer:
If the cake is cut horizontally, the cross section will be a
rectangle.
If the cake is cut vertically, the cross section will also be
a rectangle.
A solid cone is going to be sliced so that the
resulting flat portion can be dipped in paint and used
to make prints of different shapes. How should the
cone be sliced to make prints in the shape of a
triangle?
A. Cut the cone parallel to the base.
B. Cut the cone perpendicular to the
base through the vertex of the
cone.
C. Cut the cone perpendicular to the
base, but not through the vertex.
D. Cut the cone at an angle to the
base.
Use isometric dot paper to sketch a cube 2 units
on each edge.
A.
B.
C.
D.
Use isometric dot paper to sketch a triangular
prism 3 units high with two sides of the base that
are 5 units long and 2 units long.
A.
B.
C.
D.
Use isometric dot paper
and the orthographic
drawing to sketch a solid.
A.
B.
C.
D.
Describe the cross section of a rectangular solid
sliced on the diagonal.
A. triangle
B. rectangle
C. trapezoid
D. rhombus
Concept
Lateral Area of a Prism
Find the lateral area of the regular hexagonal prism.
The bases are regular
hexagons. So the
perimeter of one base is
6(5) or 30 centimeters.
Lateral area of a prism
P = 30, h = 12
Multiply.
Answer: The lateral area is 360 square centimeters.
Find the lateral area of the regular octagonal prism.
A. 162 cm2
B. 216 cm2
C. 324 cm2
D. 432 cm2
Concept
Surface Area of a Prism
Find the surface area of the rectangular prism.
Surface Area of a Prism
Surface area of a prism
L = Ph
Substitution
Simplify.
Answer: The surface area is 360 square centimeters.
Find the surface area of the triangular prism.
A. 320 units2
B. 512 units2
C. 368 units2
D. 416 units2
Concept
Lateral Area and Surface Area of a Cylinder
Find the lateral area and the surface area of the
cylinder. Round to the nearest tenth.
L = 2rh
Lateral area of a cylinder
= 2(14)(18)
Replace r with 14 and
h with 18.
≈ 1583.4
Use a calculator.
Lateral Area and Surface Area of a Cylinder
S = 2rh + 2r2
Surface area of a cylinder
≈ 1583.4 + 2(14)2
Replace 2rh with 1583.4
and r with 14.
≈ 2814.9
Use a calculator.
Answer: The lateral area is about 1583.4 square feet
and the surface area is about 2814.9 square
feet.
Find the lateral area and the surface
area of the cylinder. Round to the
nearest tenth.
A. lateral area ≈ 1508 ft2 and
surface area ≈ 2412.7 ft2
B. lateral area ≈ 1508 ft2 and
surface area ≈ 1206.4 ft2
C. lateral area ≈ 754 ft2 and
surface area ≈ 2412.7 ft2
D. lateral area ≈ 754 ft2 and
surface area ≈ 1206.4.7 ft2
Find Missing Dimensions
MANUFACTURING
A soup can is covered
with the label shown.
What is the radius of
the soup can?
L = 2rh
Lateral area of a cylinder
125.6 = 2r(8)
Replace L with 15.7 ● 8
and h with 8.
125.6 = 16r
Simplify.
2.5 ≈ r
Divide each side by 16.
Find Missing Dimensions
Answer: The radius of the soup can is about
2.5 inches.
Find the diameter of a base of a cylinder if the
surface area is 480 square inches and the height
is 8 inches.
A. 12 inches
B. 16 inches
C. 18 inches
D. 24 inches