Volume to various dimensions of cones,
pyramids, and spheres [CHALLENGE LEVEL]
EXAMPLE: (Find height of a cone.)
EXAMPLE: (Find radius of a cone.)
Suppose the volume of a cone is
423.9 cm3 and the radius is 9 cm.
What’s the height?
Suppose the volume of a cone is
307.72 m3 and the height is 6 m.
What’s the radius?
V=
1
 r2 h
3
423.9 =
1
3
1
V=
3
 r2 h
307.72 =
(3.14) (92) h
423.9 = 84.78 h
1
3
(3.14) (r2) (6)
307.72 = 6.28 r2
r2 = 307.72 / 6.28 = 49
r = √49 = 7 m
EXAMPLE: (Find height of a pyramid with EXAMPLE: (Find height of a pyramid with
a given Base.)
a Base you need to calculate.)
h = 423.9 / 84.78 = 5 cm
A rectangular pyramid with a Base (B) of
24 in2 has a volume of 56 in3. Find the
height of the pyramid.
V=
1
3
56 =
Bh
1
3
A square pyramid has a volume of 48 ft3.
Its height is 9 ft. What’s the length of each
side of the base?
V=
1
3
48 =
(24) h
Bh
1
3
B (9)
48 = 3 B
B = 48 / 3 = 16
56 = 8 h
h = 56 / 8 = 7 in.
Now B is the area of the square base, so
B = s2
16 = s2
s = √16 = 4 ft
EXAMPLE: (Find radius of a sphere.)
Suppose the volume of a sphere is 904.32 m3. What’s the radius?
V=
4
3
 r3
904.32 =
4
3
r3 = 904.32 / 4.186666667
(3.14) (r3)
904.32 = 4.186666667 r3
r3 = 216
3
r = √216 = 6 m
D. Stark 4/26/2016
YOUR TURN:
Use 3.14 for .
1) The volume of a cone is
105.504 m3 and the height is 6.3 m.
What’s the radius?
6) A hexagonal pyramid with a Base (B) of
18 in2 has a volume of 43 ½ in3. Find the
height of the pyramid.
2) A square pyramid has a volume of 32 ft3.
Its height is 6 ft. What’s the length of each
side of the base?
7) If a sphere has a volume of 3052.08 m3,
what’s the radius?
3) A triangular pyramid with a Base (B) of
81 yds2 has a volume of 432 yds3. Find the
height of the pyramid.
8) Suppose the volume of a cone is 314 ft3
and the height is 12 ft. What’s the radius?
4) A cone-shaped teepee has a diameter of
12 ft and a volume of 244.92 ft3. Could a
6’ 5” tall person stand upright under the
apex/vertex?
9) When completely filled, a cone contains
approximately 10.8 in3 of ice cream. The
5
cone is 2 in diameter. To the nearest
8
inch, how tall is it?
5) A ball holds 904.32 cubic centimeters of
air. What’s the diameter of the ball?
10) The Great Pyramid of Giza in Egypt is a
square pyramid whose sides are 755 ft and
whose volume is 91,204,000 ft3. What’s its
height?
ANSWERS: 1) 4 m 2) 4 ft 3) 16 yds 4) No. The height is 6.5 ft, which is 6’ 6”. 5) 12 cm
6) 7 ¼ in 7) 9 m 8) 5 ft 9) 6 in 10) 480 ft
D. Stark 4/26/2016