Question

a) find the volume of each cone. round your answer to two decimal places.(use $pi=3.14$)1)volume = _____________2)volume = ___________3)volume = ___________b) find the volume of each cone from the given parameters. round your answer to two decimal places. (use $pi=3.14$)4) radius = 20 ft ; height = 23 ftvolume = ___________5) height = 7 yd ; diameter = 24 ydvolume = ___________6) diameter = 19 yd ; height = 13 ydvolume = ___________7) height = 6 in ; radius = 4 involume = _____________8) the roof of a castle is in the shape of a cone. it has a height of 12 feet and a diameter 6 feet, how much air occupies the roof? (use $pi=3.14$)

Explanation:

The formula for the volume of a cone is $V = \frac{1}{3}\pi r^2 h$, where $r$ is the radius and $h$ is the height. We will apply this formula to each problem, using $\pi=3.14$ and rounding to two decimal places.

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Problem 1:

Step1: Identify $r$ and $h$

$r=5$ in, $h=8$ in

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 3.14 \times 5^2 \times 8$
$V = \frac{1}{3} \times 3.14 \times 25 \times 8 = \frac{628}{3} \approx 209.33$

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Problem 2:

Step1: Identify $r$ and $h$

$r=20$ m, $h=8$ m

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 3.14 \times 20^2 \times 8$
$V = \frac{1}{3} \times 3.14 \times 400 \times 8 = \frac{10048}{3} \approx 3349.33$

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Problem 3:

Step1: Identify $r$ and $h$

$r=14$ yd, $h=22$ yd

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 3.14 \times 14^2 \times 22$
$V = \frac{1}{3} \times 3.14 \times 196 \times 22 = \frac{13550.08}{3} \approx 4516.69$

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Problem 4:

Step1: Identify $r$ and $h$

$r=20$ ft, $h=23$ ft

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 3.14 \times 20^2 \times 23$
$V = \frac{1}{3} \times 3.14 \times 400 \times 23 = \frac{28888}{3} \approx 9629.33$

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Problem 5:

Step1: Calculate radius from diameter

$r = \frac{24}{2} = 12$ yd, $h=7$ yd

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 3.14 \times 12^2 \times 7$
$V = \frac{1}{3} \times 3.14 \times 144 \times 7 = \frac{3165.12}{3} = 1055.04$

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Problem 6:

Step1: Calculate radius from diameter

$r = \frac{19}{2} = 9.5$ yd, $h=13$ yd

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 3.14 \times 9.5^2 \times 13$
$V = \frac{1}{3} \times 3.14 \times 90.25 \times 13 = \frac{3672.145}{3} \approx 1224.05$

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Problem 7:

Step1: Identify $r$ and $h$

$r=4$ in, $h=6$ in

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 3.14 \times 4^2 \times 6$
$V = \frac{1}{3} \times 3.14 \times 16 \times 6 = 100.48$

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Problem 8:

Step1: Calculate radius from diameter

$r = \frac{6}{2} = 3$ ft, $h=12$ ft

Step2: Substitute into volume formula

$V = \frac{1}{3} \times 3.14 \times 3^2 \times 12$
$V = \frac{1}{3} \times 3.14 \times 9 \times 12 = 113.04$

Answer:

1. $209.33$ cubic inches
2. $3349.33$ cubic meters
3. $4516.69$ cubic yards
4. $9629.33$ cubic feet
5. $1055.04$ cubic yards
6. $1224.05$ cubic yards
7. $100.48$ cubic inches
8. $113.04$ cubic feet