Surface Areasof 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 drawsegments 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 eachvertex for the vertical edges.

Use Dimensions of a Solid to Sketch a Solid

Step 4 Connect the corresponding vertices. Usedashed lines for the hidden edges. Shade

thetop 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 fourstanding 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 fourthcolumn to the far right is 1 block high. The darksegments 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

infront and connect the dots on the isometric dotpaper to represent the edges of the solid.Answer:

Which diagram is the correct corner view of the figure given the orthographic drawing?

A. B.

C. D.

top view

leftview

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

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.

Answer:

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.

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?

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.

A. triangle

B. rectangle

C. trapezoid

D. rhombus

Describe the cross section of a rectangular solid sliced on the diagonal.

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.

Answer: The lateral area is 360 square centimeters.

Lateral area of a prism

P = 30, h = 12

Multiply.

A. 162 cm2

B. 216 cm2

C. 324 cm2

D. 432 cm2

Find the lateral area of the regular octagonal prism.

Concept

Surface Area of a Prism

Find the surface area of the rectangular prism.

Surface Area of a Prism

Answer: The surface area is 360 square centimeters.

Surface area of a prism

L = Ph

Substitution

Simplify.

A. 320 units2

B. 512 units2

C. 368 units2

D. 416 units2

Find the surface area of the triangular prism.

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 = 2rh 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

Answer: The lateral area is about 1583.4 square feet and the surface area is about 2814.9 square feet.

S = 2rh + 2r2 Surface area of a cylinder

≈ 1583.4 + 2(14)2 Replace 2rh with 1583.4

and r with 14.

≈ 2814.9 Use a calculator.

A. lateral area ≈ 1508 ft2 andsurface area ≈ 2412.7 ft2

B. lateral area ≈ 1508 ft2 andsurface area ≈ 1206.4 ft2

C. lateral area ≈ 754 ft2 andsurface area ≈ 2412.7 ft2

D. lateral area ≈ 754 ft2 andsurface area ≈ 1206.4.7 ft2

Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

Find Missing Dimensions

MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can?

L = 2rh Lateral area of a cylinder

125.6 = 2r(8) Replace L with 15.7 ● 8 and h with 8.

125.6 = 16r Simplify.

2.5 ≈ r Divide each side by 16.

Find Missing Dimensions

Answer: The radius of the soup can is about 2.5 inches.

A. 12 inches

B. 16 inches

C. 18 inches

D. 24 inches

Find the diameter of a base of a cylinder if the surface area is 480 square inches and the height is 8 inches.