PRACTICE: “Backwards” volume of cones, pyramids,
and spheres LEVEL 2
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
3
 r2 h
423.9 =
1
3
V=
h=
84.78
3
 r2 h
307.72 =
1
(3.14) (r2) (6)
3
307.72 = 6.28 r2
(3.14) (92) h
423.9 = 84.78 h
423.9
1
r2 =
307.72
6.28
= 5 cm
= 49
r = √49 = 7 m
EXAMPLE: (Find height of a pyramid EXAMPLE: (Find height of a pyramid
with a given Base.)
with a Base you need to calculate.)
A rectangular pyramid with a Base
(B) of 24 in2 has a volume of 56 in3.
Find the height of the pyramid.
V=
1
Bh
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=
3
1
56 = (24) h
3
h=
8
3
48 =
Bh
1
B (9)
3
48 = 3 B
56 = 8 h
56
1
B=
48
3
= 16
= 7 in.
Now B is the area of the square
base, so
B = s2
16 = s2
s = √16 = 4 ft
D. Stark 4/7/2017
“Backwards” volume of cones, pyramids, and spheres 1
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 =
(3.14) (r3)
4.186666667
r3 = 216
3
r = √216 = 6 m
904.32 = 4.186666667 r3
YOUR TURN:
904.32
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?
2) A hexagonal pyramid with a Base
(B) of 18 in2 has a volume of 43 ½ in3.
Find the height of the pyramid.
3) A square pyramid has a volume of
32 ft3. Its height is 6 ft. What’s the
length of each side of the base?
4) If a sphere has a volume of
3052.08 m3, what’s the radius?
D. Stark 4/7/2017
“Backwards” volume of cones, pyramids, and spheres 2
5) A triangular pyramid with a Base
(B) of 81 yds2 has a volume of 432
yds3. Find the height of the pyramid.
6) Suppose the volume of a cone is
314 ft3 and the height is 12 ft. What’s
the radius?
7) 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?
8) When completely filled, a cone
contains approximately 10.8 in3 of ice
5
cream. The cone is 2 in diameter.
8
To the nearest inch, how tall is it?
9) 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) 7 ¼ in 3) 4 ft 4) 9 m 5) 16 yds 6) 5 ft 7) No. The height is 6.5
ft, which is 6’ 6”. 8) 6 in 9) 12 cm 10) 480 ft
D. Stark 4/7/2017
“Backwards” volume of cones, pyramids, and spheres 3