Question

1)
volume =
2)
volume =
3)
volume =

1. height = 18 in ; radius = 12 in
2. radius = 2 ft ; height = 5 ft

for christmas, lily makes a paper cone santa hat. if the height and radius of the cone are 8 inches and 3 inches respectively, what is the volume of the hat? (use π = 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.

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1) Step1: Identify $r$ and $h$

$r=3$ in, $h=9$ in

Step1: Substitute into volume formula

$V=\frac{1}{3}\pi (3)^2 (9)$

Step2: Simplify the expression

$V=\frac{1}{3}\pi \times 9 \times 9 = 27\pi$ cubic inches

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2) Step1: Identify $r$ and $h$

$r=7$ ft, $h=11$ ft

Step1: Substitute into volume formula

$V=\frac{1}{3}\pi (7)^2 (11)$

Step2: Simplify the expression

$V=\frac{1}{3}\pi \times 49 \times 11 = \frac{539}{3}\pi$ cubic feet

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3) Step1: Identify $r$ and $h$

$r=15$ yd, $h=20$ yd

Step1: Substitute into volume formula

$V=\frac{1}{3}\pi (15)^2 (20)$

Step2: Simplify the expression

$V=\frac{1}{3}\pi \times 225 \times 20 = 1500\pi$ cubic yards

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4) Step1: Identify $r$ and $h$

$r=12$ in, $h=18$ in

Step1: Substitute into volume formula

$V=\frac{1}{3}\pi (12)^2 (18)$

Step2: Simplify the expression

$V=\frac{1}{3}\pi \times 144 \times 18 = 864\pi$ cubic inches

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5) Step1: Identify $r$ and $h$

$r=2$ ft, $h=5$ ft

Step1: Substitute into volume formula

$V=\frac{1}{3}\pi (2)^2 (5)$

Step2: Simplify the expression

$V=\frac{1}{3}\pi \times 4 \times 5 = \frac{20}{3}\pi$ cubic feet

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6) Step1: Identify $r$, $h$, and $\pi$

$r=3$ in, $h=8$ in, $\pi=3.14$

Step1: Substitute into volume formula

$V=\frac{1}{3} \times 3.14 \times (3)^2 \times 8$

Step2: Simplify the expression

$V=\frac{1}{3} \times 3.14 \times 9 \times 8 = 3.14 \times 3 \times 8 = 75.36$ cubic inches

Answer:

1. $27\pi$ cubic inches
2. $\frac{539}{3}\pi$ cubic feet
3. $1500\pi$ cubic yards
4. $864\pi$ cubic inches
5. $\frac{20}{3}\pi$ cubic feet
6. 75.36 cubic inches