Question

measurement – lesson 5
3d objects: cylinders

1. determine the surface area and volume of each cylinder. round your answer to the nearest whole number.

a.
b.

1. determine the surface area and volume of the cylinder below. express your answer for surface area in square yards and your answer for volume in cubic yards. round your answer to the nearest tenth.

Explanation:

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Part 1a: Cylinder with radius 10 in, height 26 in

Step1: Recall surface area formula

Total Surface Area (SA) of a cylinder: $SA = 2\pi r^2 + 2\pi r h$

Step2: Substitute values for SA

$SA = 2\pi(10)^2 + 2\pi(10)(26)$
$= 200\pi + 520\pi$
$= 720\pi \approx 2261.95$
Round to whole number: $2262$ square inches

Step3: Recall volume formula

Volume (V) of a cylinder: $V = \pi r^2 h$

Step4: Substitute values for V

$V = \pi(10)^2(26)$
$= 2600\pi \approx 8168.14$
Round to whole number: $8168$ cubic inches

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Part 1b: Cylinder with diameter 46 m, height 30 m

Step1: Calculate radius from diameter

Radius $r = \frac{46}{2} = 23$ m

Step2: Compute total surface area

$SA = 2\pi(23)^2 + 2\pi(23)(30)$
$= 2\pi(529) + 2\pi(690)$
$= 1058\pi + 1380\pi$
$= 2438\pi \approx 7659.58$
Round to whole number: $7660$ square meters

Step3: Compute volume

$V = \pi(23)^2(30)$
$= \pi(529)(30)$
$= 15870\pi \approx 49851.09$
Round to whole number: $49851$ cubic meters

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Part 2: Cylinder with height 18 ft (convert to yards first)

Step1: Convert units to yards

1 yard = 3 feet, so height $h = \frac{18}{3} = 6$ yd.
(Note: The radius of the cylinder is not visible in the image. For a complete solution, the radius (in feet, to convert to yards) is required. Assuming the missing radius is $r_{ft}$, converted to $r_{yd} = \frac{r_{ft}}{3}$)

Step2: Surface Area formula (yards)

$SA = 2\pi r_{yd}^2 + 2\pi r_{yd} h_{yd}$

Step3: Volume formula (yards)

$V = \pi r_{yd}^2 h_{yd}$

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Answer:

1. a.

• Surface Area: 2262 square inches
• Volume: 8168 cubic inches

1. b.

• Surface Area: 7660 square meters
• Volume: 49851 cubic meters

1. (Incomplete without radius measurement. If radius $r_{ft}$ is provided, convert to yards and use the formulas above to calculate surface area (square yards) and volume (cubic yards), rounded to the nearest tenth.)