Question

1. find the surface area of each cone. round to the nearest square unit.

a.
b.

1. calculate the volume of each cone shown below. round each answer to the tenth.

a.
b.

1. calculate the surface area and volume of each of the following cones rounded to the nearest hundredth.

a.

Explanation:

(Problem 4: Surface Area of Cones)
The total surface area of a cone is given by $SA = \pi r(r + l)$, where $r$ is the radius and $l$ is the slant height.

Part a

Step1: Identify given values

$r = 7\ \text{cm}$, $l = 19\ \text{cm}$

Step2: Substitute into surface area formula

$SA = \pi \times 7 \times (7 + 19)$
$SA = \pi \times 7 \times 26$
$SA = 182\pi \approx 182 \times 3.1416$

Step3: Calculate and round

$SA \approx 571.77$

Part b

Step1: Identify given values

$r = 27\ \text{ft}$, $l = 53\ \text{ft}$

Step2: Substitute into surface area formula

$SA = \pi \times 27 \times (27 + 53)$
$SA = \pi \times 27 \times 80$
$SA = 2160\pi \approx 2160 \times 3.1416$

Step3: Calculate and round

$SA \approx 6785.84$

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(Problem 5: Volume of Cones)
The volume of a cone is given by $V = \frac{1}{3}\pi r^2 h$, where $r$ is the radius and $h$ is the height.

Part a

Step1: Identify given values

$r = 6\ \text{in}$, $h = 9\ \text{in}$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times \pi \times 6^2 \times 9$
$V = \frac{1}{3} \times \pi \times 36 \times 9$
$V = 108\pi \approx 108 \times 3.1416$

Step3: Calculate and round

$V \approx 339.29$

Part b

Step1: Identify given values

$r = 7\ \text{ft}$, $h = 12\ \text{ft}$

Step2: Substitute into volume formula

$V = \frac{1}{3} \times \pi \times 7^2 \times 12$
$V = \frac{1}{3} \times \pi \times 49 \times 12$
$V = 196\pi \approx 196 \times 3.1416$

Step3: Calculate and round

$V \approx 615.75$

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(Problem 6: Surface Area and Volume)
First, find the height $h$ of the cone using the Pythagorean theorem: $h = \sqrt{l^2 - r^2}$, where $l=13\ \text{m}$, $r=5\ \text{m}$.

Step1: Calculate cone height

$h = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12\ \text{m}$

Surface Area

Step2: Substitute into surface area formula

$SA = \pi \times 5 \times (5 + 13)$
$SA = \pi \times 5 \times 18$
$SA = 90\pi \approx 90 \times 3.1416$

Step3: Calculate and round

$SA \approx 282.74$

Volume

Step4: Substitute into volume formula

$V = \frac{1}{3} \times \pi \times 5^2 \times 12$
$V = \frac{1}{3} \times \pi \times 25 \times 12$
$V = 100\pi \approx 100 \times 3.1416$

Step5: Calculate and round

$V \approx 314.16$

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Answer:

Problem 4

a. $572\ \text{square centimeters}$
b. $6786\ \text{square feet}$

Problem 5

a. $339.3\ \text{cubic inches}$
b. $615.8\ \text{cubic feet}$

Problem 6

Surface Area: $282.74\ \text{square meters}$
Volume: $314.16\ \text{cubic meters}$