Name __________________________________
_______________________________
Pyramids & Cones
Cones-Surface
Surface Area & Volume (12.3 & 12.5)
1. Label the height, slant height,, and base of the regular pyramid shown.
2. What kind of figure is the base?
3. What kind of figure is each lateral face?
4.
How many lateral faces does the solid have?
Find the surface area and volume of each regular pyramid by completing the steps.
5.
a. Draw and label the base.
b. Find the area of the base (B.)
f. Draw and label a lateral face.
c. Find the perimeter of the base (P.)
d. Find the height (h) of the pyramid.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h.. Find the Surface Area using SA = B + ଶ P l
6.
a. Draw and label the base.
b. Find the area of the base (B.)
f. Draw and label a lateral face.
c. Find the perimeter of the base (P.)
d. Find the height (h) of the pyramid.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ P l
a. Draw and label the base.
7.
b. Find the area of the base (B.)
f. Draw and label a lateral face.
c. Find the perimeter of the base (P.)
d. Find the height (h) of the pyramid.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ P l
8.
a. Draw and label the base.
b. Find the area of the base (B.)
f. Draw and label a lateral face.
c. Find the perimeter of the base (P.)
d. Find the height (h) of the pyramid.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ P l
9.
a. Draw and label the base.
b. Find the area of the base (B.)
f. Draw and label a lateral face.
c. Find the perimeter of the base (P.)
d. Find the height (h) of the pyramid.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ P l
10.
a. Draw and label the base.
b. Find the area of the base (B.)
f. Draw and label a lateral face.
c. Find the perimeter of the base (P.)
d. Find the height (h) of the pyramid.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ P l
11.
a. Draw and label the base.
b. Find the area of the base (B.)
Note: the base is an equilateral triangle.
f. Draw and label a lateral face.
c. Find the perimeter of the base (P.)
d. Find the height (h) of the pyramid.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ P l
12.
a. Draw and label the base.
b. Find the area of the base (B.)
f. Draw and label a lateral face.
c. Find the perimeter of the base (P.)
d. Find the height (h) of the pyramid.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ P l
Find the surface area and volume of each right cone by completing the steps.
a. Draw and label the base.
13.
b. Find the area of the base (B.)
c. Find the circumference of the base (C.)
d. Find the height (h) of the cone.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ C l
14.
a. Draw and label the base.
b. Find the area of the base (B.)
c. Find the circumference of the base (C.)
d. Find the height (h) of the cone.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ C l
a. Draw and label the base.
15.
b. Find the area of the base (B.)
c. Find the circumference of the base (C.)
d. Find the height (h) of the cone.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ C l
a. Draw and label the base.
16.
b. Find the area of the base (B.)
c. Find the circumference of the base (C.)
d. Find the height (h) of the cone.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ C l
a. Draw and label the base.
17.
b. Find the area of the base (B.)
c. Find the circumference of the base (C.)
d. Find the height (h) of the cone.
con
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ C l
a. Draw and label the base.
18.
b. Find the area of the base (B.)
c. Find the circumference of the base (C.)
d. Find the height (h) of the cone.
g. Find the slant height ( l )
ଵ
e. Find the Volume using V = ଷ B h
ଵ
h. Find the Surface Area using SA = B + ଶ C l
For each pyramid, find the value of x by completing the steps. Then identify what x represents.
19.
Volume = 80 cm3
Draw and label the base.
Find its area, or an expression for the area.
B = __________________________________
Identify the height, or an expression for the height.
h = ________________________
Substitute the expressions into the volume formula V =
1
Bh. Solve for x.
3
What does x represent?
20.
Volume = 605 m3
Draw and label the base.
Find its area, or an expression for the area.
B = __________________________________
Identify the height, or an expression for the height.
h = ________________________
Substitute the expressions into the volume formula V =
What does x represent?
1
Bh. Solve for x.
3
21.
Volume = 64 in3
Draw and label the base.
Find its area, or an expression for the area.
B = __________________________________
Identify the height, or an expression for the height.
h = ________________________
Substitute the expressions into the volume formula V =
1
Bh. Solve for x.
3
What does x represent?
22.
Volume = 56 m3
Draw and label the base.
Find its area, or an expression for the area.
B = __________________________________
Identify the height, or an expression for the height.
h = ________________________
Substitute
tute the expressions into the volume formula V =
What does x represent?
1
Bh. Solve for x.
3
For each cone, find the value of x by completing the steps. Then identify what x represents.
23.
Volume = 210 ft3
Draw and label the base.
Find its area, or an expression for the area.
B = __________________________________
Identify the height, or an expression for the height.
h = ________________________
Substitute the expressions into the volume formula V =
1
Bh. Solve for x.
3
What does x represent?
24.
Volume = 900 m3
Draw and label the base.
Find its area, or an expression for the area.
B = __________________________________
Identify the height, or an expression for the height.
h = ________________________
Substitute the expressions into the volume formula V =
1
Bh. Solve for x.
3
What does x represent?
25. A truck has hauled 48 cubic feet of sand to a building site. The sand is dumped into a conical shape 4 feet
high. What is the diameter?