Question

1. determine the surface area and volume of the rectangular prism. express your answer for surface area in square feet and for volume in cubic feet.

4 in.
24 in.
132 in.

1. calculate the surface area and volume of the cylinder. round your answer for surface area to the nearest square foot and for volume to the nearest cubic foot.

6 yd.
4 yd.

1. use the pythagorean theorem to determine the length of the missing side.

a.
40 in
42 in
b.
17 ft.
8 ft.

Explanation:

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Problem 1: Rectangular Prism

Step1: Convert inches to feet

Length: $l = \frac{132}{12} = 11$ ft, Width: $w = \frac{24}{12} = 2$ ft, Height: $h = \frac{84}{12} = 7$ ft

Step2: Calculate surface area

Surface Area formula: $SA = 2(lw + lh + wh)$
$SA = 2((11 \times 2) + (11 \times 7) + (2 \times 7)) = 2(22 + 77 + 14) = 2(113) = 226$ sq ft

Step3: Calculate volume

Volume formula: $V = lwh$
$V = 11 \times 2 \times 7 = 154$ cubic ft

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Problem 2: Cylinder

Step1: Convert yards to feet

Diameter: $d = 4 \times 3 = 12$ ft, so radius $r = \frac{12}{2} = 6$ ft; Height: $h = 6 \times 3 = 18$ ft

Step2: Calculate surface area

Surface Area formula: $SA = 2\pi r^2 + 2\pi rh$
$SA = 2\pi(6)^2 + 2\pi(6)(18) = 72\pi + 216\pi = 288\pi \approx 905$ sq ft

Step3: Calculate volume

Volume formula: $V = \pi r^2 h$
$V = \pi(6)^2(18) = 648\pi \approx 2036$ cubic ft

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Problem 3: Pythagorean Theorem

Part a

Step1: Apply Pythagorean theorem

$x = \sqrt{40^2 + 42^2}$
$x = \sqrt{1600 + 1764} = \sqrt{3364} = 58$ in

Part b

Step1: Apply Pythagorean theorem

$x = \sqrt{17^2 - 8^2}$
$x = \sqrt{289 - 64} = \sqrt{225} = 15$ ft

Answer:

1. Surface Area: 226 square feet, Volume: 154 cubic feet
2. Surface Area: 905 square feet, Volume: 2036 cubic feet
3. a. 58 inches, b. 15 feet