Question

exercises: find the volume of each cone. use either 3.14 or \\( \frac { 22 } { 7 } \\) for the value of \\( \pi \\). show formula.
1)

\\( v = \frac { 1 } { 3 } \pi r ^ { 2 } h \\)

\\( v = \\) \\( \mathrm { in } ^ { 3 } \\)

2)

\\( v = \\) \\( \mathrm { cu } \\). yd

3.) find the volume of a cone with radius 2 ft. and height 3 ft. draw and label picture if necessary.

4.) find the volume of a cone with diameter 14 yd. and height 3 yd.

5.) find the volume of a cone with radius 10 in. and height 9 in.

6.) find the volume of a cone with diameter 18 ft. and height 6 ft.

Explanation:

Step1: Volume formula for cone

The volume formula for a cone is \( V=\frac{1}{3}\pi r^{2}h \).

Step2: Solve for problem 1

Given \( r = 5\) in and \( h=7\) in. Substitute into the formula:

$$
LATEXBLOCK0
$$

Step3: Solve for problem 2

Given diameter \(d = 12\) yd, so radius \(r=\frac{d}{2}=6\) yd and \(h = 28\) yd. Substitute into the formula:

$$
LATEXBLOCK1
$$

Step4: Solve for problem 3

Given \(r = 2\) ft and \(h = 3\) ft. Substitute into the formula:

$$
LATEXBLOCK2
$$

Step5: Solve for problem 4

Given diameter \(d = 14\) yd, so radius \(r=\frac{d}{2}=7\) yd and \(h = 3\) yd. Substitute into the formula:

$$
LATEXBLOCK3
$$

Step6: Solve for problem 5

Given \(r = 10\) in and \(h = 9\) in. Substitute into the formula:

$$
LATEXBLOCK4
$$

Step7: Solve for problem 6

Given diameter \(d = 18\) ft, so radius \(r=\frac{d}{2}=9\) ft and \(h = 6\) ft. Substitute into the formula:

$$
LATEXBLOCK5
$$

Answer:

1. \(183.17\) in³
2. \(1056\) cu.yd
3. \(12.56\) ft³
4. \(154\) yd³
5. \(942\) in³
6. \(508.68\) ft³