3D Shapes

Cylinders

100

How do you find the volume of a cylinder?

Area_Circle X Height

200

What shapes make up the net of a cylinder?

Two Circles

One Rectangle

300

Find the volume of a cylinder that has a height of 5 in and a radius 2.7 in.

V=A_o X Height

A_o= Pi X 2.7²=22.9

V=22.9 X 5=114.5

400

Find the surface area of a cylinder that has a height of 24 mm and a diameter of 53 mm.

R=53/2

A_o=Pi X 26.5²=2206.1

C=53 X Pi=166.5

A_Rectangle=166.5 X 24=3996

SA=2 X 2206.1 + 3996=8408.2

500

What would the height of a cylinder need to be if the radius is 7 ft and the volume is 923.6 cubed ft.

V=A_o X Height

V/A_o=Height

A_o=Pi X 7²=153.9

Height=923.6/153.9=6

Prims

100

How do you find the volume of a prism?

Area_Base X Height

200

What is the base shape of a triangular prism?

A triangle

300

Find the volume of a rectangular prism with a height of 12 ft, a length of 4 ft, and a width of 9 ft.

V=12 X 4 X 9=432

400

Find the surface area of Figure 2 on the right board.

45.78

500

If the base side lengths of a hexagonal prism are 7 m and the height of the prism is 12 m, what would the volume of the prism be?

1512 cubed meters

Cones

100

How do you find the volume of a cone?

Area_Circle X Height / 3

200

What shapes make up the net of a cone?

A full circle and a pac-man circle.

300

Find the volume of a cone that has a height of 11 cm and a radius of 5 cm.

V= A_o X Height/3

A_o=Pi X 5²=78.5

V=78.5 X 11/3=287.8

400

How do you find the area of the pac-man sector?

Take the circumferences of both circles and divided them, then multiply that number by the area of the pac-man circle.

500

Given a cone that has a volume of 333 cubed cm with a radius of 4 cm, what would the height of the cone be?

V=A_o X Height/3

V X 3=A_o X Height

V X 3/A_o=Height

A_o=Pi X 4²=50.2

Height=333 X 3/50.2=19.9

Pyramids

100

How do you find the volume of a pyramid?

Area_Base X Height / 3

200

If a pyramid has a rectangle as it's base, what shapes would make up the net?

4 Triangles

1 Rectangle

300

If a pyramid has a heptagon as it's base, what shapes would make up the net?

7 Triangles

1 Heptagon

400

Find the volume of Figure 1 on the left board.

242.6

500

Find the surface area of Figure 1 on the left board.

258

Spheres

100

How do you find the volume of a sphere?

(2/3) X Pi X R² X Height

200

How do you find the surface area of a sphere?

4 X Pi X R²

300

Find the volume of a sphere that has a height of 18 cm.

V=(2/3) X Pi X R² X Height

Height=Diameter

R=18/2=9

V=(2/3) X Pi X 9² X 18=3053.6

400

Find the surface area of a half sphere that has a radius of 33 mm.

Total SA=SA X A_o

SA=4 X Pi X 33²/2=6842.35

A_o=Pi X 33²=3421.1

Total SA=6842.35+3421.1=10263.45

500

What would the radius of a sphere need to be if the surface area is 100 square in?

4 X Pi X R² = SA

Pi X R²=SA/4

R²=SA/(4Pi)

R=Sqrt(SA/(4Pi))

R=Sqrt(100/(4Pi))=2.8