Question

4)
volume =
(image of a cone with diameter 8.8 in and slant height 9.1 in? wait, no, the height? wait, the diagram shows a cone with a diameter of 8.8 in (so radius is 4.4 in) and a height? wait, maybe the 9.1 in is the height? wait, the ocr text from the image: the cone has 8.8 in (diameter) and 9.1 in (maybe height). then 5)
volume =
(image of a cone with height 14.6 m and diameter... wait, the diagram has 14.6 m (maybe height) and a radius? wait, the text on the cone: 14.6 m and 6.2 m? wait, maybe radius 6.2 m? then 6)
volume =
(image of a cone with radius 1.2 cm and height 5.9 cm)

Explanation:

Problem 4 (Cone with diameter 8.8 in, height 9.1 in)

Step 1: Find the radius

The diameter is 8.8 in, so the radius \( r=\frac{8.8}{2}=4.4 \) in.

Step 2: Use the cone volume formula

The volume of a cone is \( V = \frac{1}{3}\pi r^{2}h \). Substitute \( r = 4.4 \) in, \( h=9.1 \) in, and \( \pi\approx3.14 \).
\( V=\frac{1}{3}\times3.14\times(4.4)^{2}\times9.1 \)
First, calculate \( (4.4)^{2}=19.36 \)
Then, \( 3.14\times19.36 = 60.7904 \)
Next, \( 60.7904\times9.1 = 553.19264 \)
Finally, \( \frac{1}{3}\times553.19264\approx184.4 \) cubic inches.

Step 1: Find the radius

The diameter is 6.2 m, so the radius \( r=\frac{6.2}{2}=3.1 \) m.

Step 2: Use the cone volume formula

The volume of a cone is \( V=\frac{1}{3}\pi r^{2}h \). Substitute \( r = 3.1 \) m, \( h = 14.6 \) m, and \( \pi\approx3.14 \).
\( V=\frac{1}{3}\times3.14\times(3.1)^{2}\times14.6 \)
First, calculate \( (3.1)^{2}=9.61 \)
Then, \( 3.14\times9.61 = 30.1754 \)
Next, \( 30.1754\times14.6 = 440.56084 \)
Finally, \( \frac{1}{3}\times440.56084\approx146.85 \) cubic meters.

Step 1: Use the cone volume formula

The volume of a cone is \( V=\frac{1}{3}\pi r^{2}h \). Substitute \( r = 1.2 \) cm, \( h = 5.9 \) cm, and \( \pi\approx3.14 \).
\( V=\frac{1}{3}\times3.14\times(1.2)^{2}\times5.9 \)
First, calculate \( (1.2)^{2}=1.44 \)
Then, \( 3.14\times1.44 = 4.5216 \)
Next, \( 4.5216\times5.9 = 26.67744 \)
Finally, \( \frac{1}{3}\times26.67744\approx8.89 \) cubic centimeters.

Answer:

\( \approx184.4 \) cubic inches

Problem 5 (Cone with diameter 6.2 m, height 14.6 m)