PRACTICE: “Backwards” volume of cones, pyramids, and spheres

PRACTICE: “Backwards” volume of cones, pyramids, and spheres Use 3.14 for . EXAMPLE 1: (Find height of a cone.) Suppose the volume of a cone is 423.9 cm3 and the radius is 9 cm. What’s the height? .

V=

1 3

 r2 h

423.9 =

1 3

EXAMPLE 2: (Find radius of a cone.) Suppose the volume of a cone is 307.72 m3 and the height is 6 m. What’s the radius? .

V=

h=

84.78

(3.14) (92) h

r2 =

Bh 3 1 56 = (24)h 3 56 = 8h h=

8

6.28

= 7 in.

= 49

r = √49 = 7 m

A rectangular pyramid with a Base (B) of 24 in2 has a volume of 56 in3. Find the height of the pyramid.

56

307.72

= 5 cm

1

1

(3.14) (r2) (6) 3 307.72 = 6.28 r2

EXAMPLE 3 : (Find height of a pyramid with a given Base.)

V=

3

 r2 h

307.72 =

423.9 = 84.78 h

423.9

1

EXAMPLE 4: (Find height of a pyramid with a Base you need to calculate.) 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 =

Bh

1

B(9) 3 48 = 3 B B=

48 3

= 16

Now B is the area of the square base, so B = s2 16 = s2 s = √16 = 4 ft © D. Stark 2017 10/14/2017

PRACTICE: “Backwards” vol. of cones, pyramids, & spheres 1

EXAMPLE 5: (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

904.32 = 4.186666667 r3

YOUR TURN:

904.32

3

r = √216 = 6 m

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 2017 10/14/2017

PRACTICE: “Backwards” vol. of cones, pyramids, & 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 2017 10/14/2017

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