A cone has a radius of 4 feet on its base. The approximate volume of the cone is 189 ft^3. Determine the height of the cone to the nearest tenth of a foot. Use 3.14 for π.(5 points)

Question

A. Use this formula: Responce Area

B. Substitute in for the radius and simplify to get Responce Area


C. Use the reciprocal to get about Responce Area


D. Use the inverse operation of Responce Area to get h by itself.

D. Height is approximately Responce Area

responce A:
V = 4/3 pi r^3
A = pi r^2
V = pi r^2 h
V= 1/3 pi r^2 h

responce B:
189 = 8/3 pi h
189 = 64/3 pi h
189 = 16/3 pi h
189 = 16 pi h

responce C:
1008 = pi h
504 = pi h
35.4 = pi h
23.6 = pi h

responce D:
subtraction
addition
multiplication
division

responce D:
8.2 ft
11.3 ft
2.5 ft
22.6 ft

Answer 1

To determine the height of the cone, let's go through the steps methodically and fill in the responses.

A. Use this formula: \[ V = \frac{1}{3} \pi r^2 h \]

B. Substitute in for the radius and simplify to get \[ 189 = \frac{1}{3} \pi (4^2) h \] \[ 189 = \frac{1}{3} \pi (16) h \] \[ 189 = \frac{16}{3} \pi h \]

Now, by substituting \( \pi \approx 3.14 \): \[ 189 = \frac{16}{3} (3.14) h \] \[ 189 = \frac{50.24}{3} h \] \[ 189 = 16.7433 h \] (approximately)

C. Use the reciprocal to get about \[ h = \frac{189}{16.7433} \approx 11.3 , \text{ft} \] (to 1 decimal place)

D. Use the inverse operation of To isolate \( h \), we will divide both sides by \( 16.7433 \): \[ h = \frac{189}{16.7433} \]

D. Height is approximately \[ h \approx 11.3 , \text{ft} \] (to the nearest tenth of a foot)

Thus, to summarize:

• Response A: \( V = \frac{1}{3} \pi r^2 h \)
• Response B: \( 189 = \frac{16}{3} \pi h \)
• Response C: \( h \approx 11.3 , \text{ft} \)
• Response D: Height is approximately \( 11.3 , \text{ft} \)